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NO.  94-821 97 


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Author: 


Wentworth,  George  Albert 


Title: 


Five-place  logarithmic  and 

trigonometric  tables 

Place: 

Boston 

Date: 

1895 


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MASTER   NEGATIVE  # 


COLUMBIA  UNIVERSITY  LIBRARIES 
PRESERVATION  DIVISION 

BIBLIOGRAPHIC  MICROFORM  TARGET 


ORIGINAL  MATERIAL  AS  FILMED  -    EXISTING  BIBLIOGRAPHIC  RECORD 


485.'"'"''" 
W48    ' 


Wentworth,  George  Albert,  1835-1906. 

* 

Five-place  logarithmic  and  trigonometric  tables  ar- 
ranged by  6.  A.  Wentworth,  a.  m.,  and  G.  A.  Hill,  a.  m. 
Boston  and  London,  Giim  &  company^  1895., 

XX,  75  p.    23J*"".    (/»-*«" Plane-and-spherical  trigonetnetry  and  tables.-- 
Boston  aml"t>ondotv^89§^)- 


1842- 


1.  Logarithms.    2.  Trigonometry— Tables,  etc.      i.  Hill,  George  Anthony, 

12—  ininf  aiitVin?  •""■■ 


joint  authoT. 


Library  of  Congress 


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FILMED  BY  PRESERVATION  RESOURCES.  BETHLEHEM,  PA. 


BIBLIOGRAPHIC  IRREGULARITIES 

MAIN  ENTRY:    Wentworth.  Georae  Albert 


Five-place  logarithmic  and  trigonometric  tables 


Bibliographic  Irregularities  in  the  Original  Document: 

List  all  volumes  and  pages  affected;  include  name  of  institution  if  filming  borrowed  text 


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pages  44-61 — 


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FIVE-PLACE  LOGARITHMIC  AND 
TRIGONOMETRIC  TABLES 


ARRANGED  BY 

G.  A.  WENTWORTH,  A.M. 

AND 

G.  A.  HILL,  A.M= 


GINN  AND  COMPANY 

BOSTON     •     NEW   YORK     •     CHICAGO     •     LONDON 
ATLANTA     •    DALLAS    ^     COLUMBUS     •    SAN   FRANCISCO 


V 

;■ 


\ 


INTRODnOTIOK 


Entered,  aocording  to  Act  of  CJongress,  in  the  year  1882,  by 

G.  A.  WENTWORTH  and  G.  A.  HILL 
in  the  Office  of  the  Librarian  of  Ck}ngress,  at  Washington 


Copyright,  1895,  by. 
G.  A.  WENTWORTH  and  G.  A.  HILL 


ALL  RIGHTS  RESERVED 
420.4 


1.  If  the  natural  numbers  are  regarded  as  powers  of  ten,  the 
exponents  of  the  powers  are  the  Common  or  Briggs  Logarithms  of 
the  numbers.  If  A  and  B  denote  natural  numbers,  a  and  b  their 
logarithms,  then  W  =  A,  10^  =  B;  or,  written  in  logarithmic  form, 

log-4  =  a,        \ogB=^b. 

2.  The  logarithm  of  a  product  is  found  by  adding  the  logarithms 
of  its  factors. 

For,  AX  B  =  10«  X  106  =  10«  +  ^ 

Therefore,  log{A  x  B)  =  a  +  b  =  \ogA-^  log B. 

3.  The  logarithm  of  a  quotient  is  found  by  subtracting  the 
logarithm  of  the  divisor  from  that  of  the  dividend. 

Therefore,  log  —  =  a  —  6  =  log  J.  —  log  B, 

4.  The  logarithm  of  a  power  of  a  number  is  found  by  multiply- 
ing the  logarithm  of  the  number  by  the  exponent  of  the  power. 

For,  A«  =  (JP")"  =  10«». 

Therefore,  log-^l"  =  an  =  n  log  A, 


5.   The  logarithm  of  the  root  of  a  number  is  found  by  dividing 
the  logarithm  of  the  number  by  the  index  of  the  root. 


For, 
Therefore, 


y/A  =  \^  =  10^. 


etc  nthttiKum  ^re<g 

GINN  AND  COMPANY  •  PRO- 
PRIETORS •  BOSTON  •  U.S.A. 


6.  The  logarithms  of  1,  10,  100,  etc.,  and  of  0.1,  0.01,  0.001, 
etc.,  are  integral  numbers.  The  logarithms  of  all  other  numbers 
are  fractions. 


J?4 


!▼ 


LOGARITHMS. 


lor,   10»=       1,  hence       logl  =  0 

101  =     10,  hence     log  10  =  1 

102  =    100,  hence    log  100  =  2 
108  =  1000,  hence  log  1000  =  3 

If  the  number  is  between  1  and  10, 

If  the  number  is  between  10  and  100, 

If  the  number  is  between  100  and  1000, 

If  the  number  is  between  1  and  0.1, 

If  the  number  is  between  0.1  and  0.01, 

If  the  number  is  between  0.01  and  0.001, 
And  so  on. 


10-1  =     0.1,  hence     logO.l  =  —  1 ; 

10-2  =   0.01,  hence    log  0.01  =  —  2 ; 

10-«  =  0.001,  hence  log  0.001  =  —  3 ; 

and  so  on. 

the  logarithm  is  between 
the  logarithm  is  between 


the  logarithm  is  between 


0  and  1. 
land  2. 
2  and  3. 
0  and  —1. 


the  logarithm  is  between 

the  logarithm  is  between  —1  and  —2. 

the  logarithm  is  between  —2  and  —3. 


. 


7.  If  the  number  is  less  than  1,  the  logarithm  is  negative  (§  6)j 
but  is  written  in  such  a  form  that  t\iQ  fractional  part  is  always  ^osi^ive. 

For  the  number  may  be  regarded  as  the  product  of  two  factors,  one  of 
which  lies  between  1  and  10,  and  the  other  is  a  negative  power  of  10 ;  the 
logarithm  will  then  take  the  form  of  a  difference  whose  minuend  is  a  positive 
proper  fraction,  and  whose  subtrahend  is  a  positive  integral  number. 

Thus,  0.48  =  4.8  X  0.1. 

Therefore  (§  2),  log     0.48  =  log  4.8  +  log  0.1  =  0.68124  —  1.     (Page  1.) 

Again,  0.0007  =  7  X  0.0001. 

Therefore,  log  0.0007  =  log  7  +  log  0.0001  =  0. 84510  —  4. 

The  logarithm  0.84510  —  4  is  often  written  5.84510. 

8.  Every  logarithm,  therefore,  consists  of  two  parts  :  a  positive 
or  negative  integral  number,  which  is  called  the  Characteristic,  and 
a  positive  proper  fraction,  which  is  called  the  Mantissa. 

Thus,  in  the  logarithm  3.62179,  the  integral  number  3  is  the  characteristic, 
and  the  fraction  .52179  the  mantissa..  In  the  logarithm  0.78254  —  2,  the  inte- 
gral number  —  2  is  the  characteristic,  and  the  fraction  0.78264  is  the  mantissa. 

9.  If  the  logarithm  is  negative,  it  is  customary  to  change  the 

form  of  the  difference  so  that  the  subtrahend  shall  be  10  or  a  multiple 

of  10.     This  is  done  by  adding  to  both  minuend  and  subtrahend  a 

number  which  will  increase  the  subtrahend  to  10  or  a  multiple  of  10. 

Thus,  the  logarithm  0.78264  —  2  is  changed  to  8.78264  —  10  by  adding  8  to 
both  minuend  and  subtrahend.  The  logarithm  0.92737  — 13  is  changed  to 
7.92737  —  20  by  adding  7  to  both  minuend  and  subtrahend. 

10.  The  following  rules  are  derived  from  §  6 :  — 

If  the  number  is  greater  than  1,  make  the  characteristic  of  the 
logarithm  one  unit  less  than  the  number  of  figures  on  the  left  of 
the  decimal  point. 

If  the  number  is  less  than  1,  make  the  characteristic  of  the  loga- 
rithm negative,  and  one  unit  more  than  the  number  of  zeros  between 
the  decimal  point  and  the  first  significant  figure  of  the  'given  number. 


INTRODUCTION. 


If  the  characteristic  of  a  given  logarithm  is  positive,  make  the 
number  of  figures  in  the  integral  part  of  the  corresponding  number 
one  more  than  the  number  of  units  in  the  characteristic. 

If  the  characteristic  is  negative,  make  the  number  of  zeros  between 
the  decimal  point  and  the  first  significant  figure  of  the  correspond- 
ing number  one  less  than  the  number  of  units  in  the  characteristic. 

Thus,  the  characteristic  of  log  7849.27  =  3 ; 

the  characteristic  of  log  0.037  =  -  2  =  8.00000  —  10. 
If  the  characteristic  is  4,  the  corresponding  number  has  five  figures  in  its  inte- 
gral part.     If  the  characteristic  is  -  3,  that  is,  7.00000  -  10,  the  corresponding 
fraction  has  two  zeros  between  the  decimal  point  and  the  first  significant  figure. 

11.  The  logarithms  of  numbers  that  can  be  derived  one  from 
another  by  multiplication  or  division  by  an  integral  power  of  10 
have  the  same  mantissa. 

For,  multiplying  or  dividing  a  number  by  an  integral  power  of  10  will 
increase  or  diminish  its  logarithm  by  the  exponent  of  that  power  of  10 ;  and 
since  this  exponent  is  an  integer,  the  mantissa  of  the  logarithm  will  be 
unaffected. 


Thus, 


log  4.6021 
log  460.21 

log  460210 

log  0.046021 


0.66296.     (Page  9.) 

log  (4.6021  X  102)  =  log  4.6021  +  log  10^ 
0.66296  +  2  =  2.66296. 
:  log  (4.6021  X  105)  =  log  4.6021  +  log  10^ 
0.66296  +  5  =  5.66296. 
:  log  (4.6021  -r  102)  =  log  4.6021  -  log  10» 
0.66296  —  2  =  8.66296  —  10. 


TABLE  I. 

12.  In  this  table  (pp.  1-19)  the  vertical  columns  headed  N  con- 
tain the  numbers,  and  the  other  columns  the  logarithms.  On  page  1 
both  the  characteristic  and  the  mantissa  are  printed.  On  pages 
2-19  the  mantissa  only  is  printed. 

The  fractional  part  of  a  logarithm  can  be  expressed  only  approx- 
imately, and  in  a  five-place  table  all  figures  that  follow  the  fifth  are 
rejected.  Whenever  the  sixth  figure  is  5,  or  more,  the  fifth  figure 
is  increased  by  1.  The  figure  5  is  written  when  the  value  of  the 
figure  in  the  place  in  which  it  stands,  together  with  the  succeeding 
figures,  is  more  than  4^,  but  less  than  5. 

Thus,  if  the  mantissa  of  a  logarithm  written  to  seven  places  is  5328732,  it  is 
written  in  this  table  (a  five-place  table)  53287.  If  it  is  5328751,  it  is  written 
53288.     If  it  is  5328461  or  5328499,  it  is  written  in  this  table  53285. 

Again,  if  the  mantissa  is  5324981,  it  is  written  63260 ;  and  if  it  is  4999967,  it 
is  written  60000. 


VI 


LOGARITHMS. 


INTRODUCTION. 


VU 


This  distinction  between  6  and  5,  in  case  it  is  desired  to  curtail 
still  further  the  mantissas  of  logarithms,  removes  all  doubt  whether 
a  5  in  the  last  given  place,  or  in  the  last  but  one  followed  by  a 
zero,  should  be  simply  rejected,  or  whether  the  rejection  should 
lead  us  to  increase  the  preceding  figure  by  one  unit. 

Thus,  the  mantissa  13925  when  reduced  to  four  places  should  be  1392 ;  but 
13925  should  be  1393. 

To  Find  the  Logarithm  of  a  Given  Number. 

13.  If  the  given  number  consists  of  one  or  two  significant 
figures,  the  logarithm  is  given  on  page  1.  If  zeros  follow  the  sig- 
nificant figures,  or  if  the  number  is  a  proper  decimal  fraction,  the 
characteristic  must  be  determined  by  §  10. 

14.  If  the  given  number  has  three  significant  figures,  it  will  be 
found  in  the  column  headed  N  (pp.  2-19),  and  the  mantissa  of  its 
logarithm  in  the  next  column  to  the  right,  and  on  the  same  line. 

Thus, 

Page    2.        log  145  =  2.16137,  log  14500  =  4.16137. 

Page  14.         log  716  =  2.85491,  log  0.716  =  9.85491  -  10. 

15.  If  the  given  number  ha»  four  significant  figures,  the  first 

three  will  be  found  in  the  column  headed  N,  and  the  fourth  at  the 

top  of  the  page  in  the  line  containing  the  figures  1,  2,  3,  etc.     The 

mantissa  will  be  found  in  the  column  headed  by  the  fourth  figure, 

and  on  the  same  line  with  the  first  three  figures.     Thus, 

Page  15.     log  7682    =3.88547,        log  76.85    =1.88564. 
Page  18.     log  93280  =  4.96979,         log  0.9468  =  9.97626  -  10. 

16.  If  the  given  number  has  five  or  more  significant  figures,  a 
process  called  interpolation  is  required. 

Interpolation  is  based  on  the  assumption  that  between  two  con- 
secutive mantissas  of  the  table  the  change  in  the  mantissa  is  directly 
proportional  to  the  change  in  the  number. 

Required  the  logarithm  of  34237. 

The  required  mantissa  is  (§  11)  the  same  as  the  mantissa  for  8423. 7  ;  there- 
fore it  will  be  found  by  adding  to  the  mantissa  of  3423  seven-tenths  of  the 
difference  between  the  mantissas  for  3423  and  3424. 

The  mantissa  for  3423  is  53441. 

The  difference  between  the  mantissas  for  3423  and  3424  is  12. 

Hence,  the  mantissa  for  3423.7  is  53441  +  (0.7  x  12)  =  53449. 

Therefore,  the  required  logarithm  of  34237  is  4.53449. 


\ 


Required  the  logarithm  of  0.0015764. 

The  required  mantissa  is  the  same  as  the  mantissa  for  1576.4;  therefore 
It  will  be  found  by  adding  to  the  mantissa  for  1576  four-tenths  of  the  difference 
between  the  mantissas  for  1576  and  1577. 

The  mantissa  for  1576  is  19756. 

The  difference  between  the  mantissas  for  1576  and  1577  is  27. 
.      Hence,  the  mantissa  for  1576.4  is  19756  +  (0.4  x  27)  =  19767. 

Therefore,  the  required  logarithm  of  0.0015764  is  7.19767  — 10. 

Required  the  logarithm  of  32.6708. 

The  required  mantissa  is  the  same  as  the  mantissa  for  3267.08 ;  therefore 
it  will  be  found  by  adding  to  the  mantissa  for  3267  eight-hundredths  of  tho 
difference  between  the  mantissas  for  3267  and  3268. 

The  mantissa  for  3267  is  51415. 

The  difference  between  the  mantissas  for  3267  and  3268  is  13. 

Hence,  the  mantissa  for  3267.08  is  51415  +  (0.08  x  13)  =  61416. 

Therefore,  the  required  logarithm  of  32.6708  is  1.61416.  • 

17.  When  the  fraction  of  a  unit  in  the  part  to  be  added  to  the 
mantissa  for  four  figures  is  less  than  0.5  it  is  to  be  neglected  j  when 
it  is  0.5  or  more  than  0.5  it  is  to  be  taken  as  one  unit. 

Thus,  in  the  first  example,  the  part  to  be  added  to  the  mantissa  for  3423  is 
8.4,  and  the  .4  is  rejected.  In  the  second  example,  the  part  to  be  added  to  the 
mantissa  for  1676  is  10.8,  and  11  is  added. 

To  Find  the  Antilogarithm  ;    that  is,  the  Number  Corrb- 

SPONDING   TO    A    GiVEN    LOGARITHM. 

18.  If  the  given  mantissa  can  be  found  in  the-  table,  the  first 
three  figures  of  the  required  number  will  be  found  in  the  same  line 
with  the  mantissa  in  the  column  headed  N,  and  the  fourth  figure  at 
the  top  of  the  column  containing  the  mantissa. 

The  position  of  the  decimal  point  is  determined  by  the  charac- 
teristic (§  10). 

Find  the  number  corresponding  to  the  logarithm  0.92002. 

Page  16.    The  number  for  the  mantissa  92002  is  8318. 

The  characteristic  is  0 ;  therefore,  the  required  number  is  8.318. 

Find  the  number  corresponding  to  the  logarithm  6.09167, 

Page  2.     The  number  for  the  mantissa  09167  is  1235. 

The  characteristic  is  6 ;  therefore,  the  required  number  is  1235000. 

Find  the  number  corresponding  to  the  logarithm  7.50325  — 10. 

Page  6.     The  number  for  the  mantissa  60326  is  3186. 

The  characteristic  is  —  3 ;  therefore,  the  required  number  is  0.003186. 


tl 


VIU 


LOOABITHMS. 


19.  If  the  given  mantissa  cannot  be  found  in  the  table,  find 
in  the  table  the  two  adjacent  mantissas  between  which  the  given 
mantissa  lies,  and  the  four  figures  corresponding  to  the  smaller  of 
these  two  mantissas  will  be  the  first  four  significant  figures  of  the 
required  number.  If  more  than  four  figures  are  desired,  they  may- 
be found  by  interpolation,  as  in  the  foUowiag  examples : 

Find  the  number  corresponding  to  the  logarithm  1.48762. 

Here  the  two  adjacent  mantissas  of  the  table,  between  which  the  given  man- 
tissa 48762  lies,  are  found  to  be  (page  6)  48756  and  48770.  The  corresponding 
numbers  are  3073  and  3074.  The  smaller  of  these,  3073,  contains  the  first  four 
significant  figures  of  the  required  number. 

The  difference  between  the  two  adjacent  mantissas  is  14,  and  the  difference 
between  the  corresponding  numbers  is  1. 

The  difference  between  the  smaller  of  the  two  adjacent  mantissas,  48756, 
and  the  given  toantissa,  48762,  is  6.  Therefore,  the  number  to  be  annexed  to 
3073  is  t\  of  1  =  0.428,  and  the  fifth  significant  figure  of  the  required  number 

18  4. 

Hence,  the  required  number  is  30.734. 

Find  the  number  corresponding  to  the  logarithm  7.82326  — 10. 

The  two  adjacent  mantissas  between  which  82326  lies  are  (page  13)  82321 
and  82328.     The  number  corresponding  to  the  mantissa  82321  is  6656. 

The  difference  between  the  two  adjacent  mantissas  is  7,  and  the  difference 
between  the  corresponding  numbers  is  1. 

The  difference  between  the  smaller  mantissa,  82321,  and  the  given  mantissa, 
82326,  is  5.  Therefore,  the  number  to  be  annexed  to  6656  is  f  of  1  =  0.7,  and 
the  fifth  significant  figure  of  the  required  number  is  7. 

Hence,  the  required  number  is  0.0066567. 

In  using  a  five-place  table  the  numbers  corresponding  to  man- 
tissas may  be  carried  to  five  significant  figures,  and  in  the  first 
part  of  the  table  to  six  figures.* 

20.  The  logarithm  of  the  reciprocal  of  a  number  is  called  the 
Cologarithm  of  the  number. 

If  A  denotes  any  number,  then 

colog  ^  =log  -\~^^%  1  — log  ^  (§  3)  =  — log  A. 

Hence,  the  cologarithm  of  a  number  is  equal  to  the  logarithm  of 
the  number  with  the  minus  sign  prefixed,  whwh  sign  affects  the 
entire  logarithm^  both  characteristic  and  mantissa. 

*In  most  tables  of  logarithms  proportional  parts  are  given  as  an  aid  to 
interpolation ;  but,  after  a  little  practice,  the  operation  can  be  performed  nearly 
as  rapidly  without  them.  Their  omission  allows  a  page  with  larger-faced  type 
and  more  open  spacing,  and  consequently  less  trying  to  the  eyes. 


INTRODUCTION. 


IX 


In  order  to  avoid  a  negative  mantissa  in  the  cologarithm,  it  is 
customary  to  substitute  for  —  log  A  its  equivalent 

(10 -log -4)  — 10. 

Hence,  the  cologarithm  of  a  number  is  found  by  subtracting  the 
logarithm  of  the  number  from  10,  and  then  annexing  — 10  to  the 

remainder. 

The  best  way  to  perform  the  subtraction  is  to  begin  on  the  left 
and  subtract  each  figure  of  log  A  from  9  until  we  reach  the  last 
significant  figure,  which  must  be  subtracted  from  10. 

If  log  A  is  greater  in  absolute  value  than  10  and  less  than  20, 
then  in  order  to  avoid  a  negative  mantissa,  it  is  necessary  to  write 

—  log  A  in  the  form 

(20— log  ^y— 20. 

So  that,  in  this  case,  colog  A  is  found  by  subtracting  log  A  from 
20,  and  then  annexing  —20  to  the  remainder. 


Find  the  cologarithm  of  4007. 

10  -10 

Page  8.  log  4007  =    3.60282 

colog  4007=    6.39718  —  10 

Find  the  cologarithm  of  103992000000. 

20  —  20 

Page  2.     log  103992000000  =  11.01700 

colog  103992000000  =    8.98300  -  20 

If  the  characteristic  of  log  A  is  negative,  then  the  subtrahend, 
10  or  —  20,  will  vanish  in  finding  the  value  of  colog  A, 


10 

10 


Find  the  cologarithm  of  0.004007. 

10 

log  0.004007  =    7.60282 
colog  0.004007  =    2.39718 


With  practice,  the  cologarithm  of  a  number  can  be  taken  from 
the  table  as  rapidly  as  the  logarithm  itself. 

By  using  cologarithms  the  inconvenience  of  subtracting  the  log- 
arithm of  a  divisor  is  avoided.  For  dividing  by  a  number  is 
equivalent  to  multiplying  by  its  reciprocal.  Hence,  instead  of 
subtracting  the  logarithm  of  a  divisor  its  cologarithm  may  be 
added. 


LOGABITHMS. 


EXEBCISES. 


Knd  the  logarithms  of : 


1.  6170. 

2.  0.617. 

3.  2867. 


4.  85.76. 
6.  296.8. 
6.  7004. 


7.  0.8694. 

8.  0.5908. 

9.  73243. 


10.  67.3208. 

11.  18.5283. 

12.  0.004200a 


Find  the  cologarithms  of : 


13.  72433. 

14.  802.376. 
16.  15.7643. 


16.  869.278. 

17.  154000. 

18.  70.0426. 


19.  0.002403. 

20.  0.000777. 

21.  0.051828. 


Find  the  antilogarithms  of,: 


22.  2.47246. 

23.  7.89081. 

24.  2.91221. 


26.    1.26784. 

26.  3.79029. 

27.  6.18752. 


28.  9.79029—10. 

29.  7.62328  —  10. 

30.  6.15466-10. 


Computation  by  Logabithms. 

21.    (1)  Find  the  value  of  a;,  if  a;  =  72214  X  0.0820a 

Page  14.  log  72214     =  4.85862 

Page  16.  log  0.08203  =  8.91397  —  10 

By  §2.  logx  =3.77259 

Page  11.  X  =  5923.63 


(2)  Find  the  value  of  a;,  if  a;  =  5250  ^  23487. 


Page  10. 
Page  4. 
Page  4. 


log  5250 
colog  23487 
logx 

.'.X 


=  3.72016 

=  5.62917  —  10 


(3)  Find  the  value  of  a;,  if  «  = 


Page  15. 
Page  9. 
Page  11. 
Page  17. 
Page  6. 
Page  4. 
Page  6. 


log  7.56 

log  4667 

log  567 
colog  899.1 
colog  0.00337 
colog  23435 

logx 
.'.X 


=  9.34933  -  10  =  log  0.22353 
=  0.22353 

7.56  X  4667  X  567 

899.1  X  0.00337  X  23435 

=  0.87852 

=  3.66904 

=  2.75358 

=  7.04619-10 

=  2.47237 

=  6.63013  - 10 

2.44983  =  log  281.73 
281.73. 


INTBODUCTION. 


(4)  Find  the  cube  of  376. 

Page  7.  log  376 

Multiply  by  3  (§  4), 
Page  10.  log  3768 

.-.  3763 


=  2.57619 
3 

=  7.72557  =  log  53158600 
=  53158600. 


(5)  Find  the  square  of  0.003278. 


Page  6. 
Page  2. 


log  0.00^78  =    7.51661  -  10 


log  0.0032782  =  15.03122  —  20  =  log  0.000010746 
.-.0.0032782=    0.000010745. 


(6)  Find  the  square  root  of  8322. 


Page  16.  log  8322 

Divide  by  2  (§  5), 


=  3.92023 
2)3.92023 


log  V8322      =  1.96012  =  log  91.226 
.-.  >^322     =  91.226. 

If  the  given  number  is  a  proper  fractiou,  its  logarithm  will  have 
as  a  subtrahend  10  or  a  multiple  of  10.  In  this  case,  before  divid- 
ing the  logarithm  by  the  index  of  the  root,  both  the  subtrahend  and 
the  number  preceding  the  mantissa  should  be  increased  by  such  a 
number  as  will  make  the  subtrahend,  when  divided  by  the  index  of 
the  root,  10  or  a  multiple  of  10. 

(7)  Find  the  square  root  of  0.000043641. 

Page  8.  log 0.000043641     =    6.63989—10 

10  -10 

Divide  by  2  (§  5),      2)15.63989-20 

Page  13.  log  VO.000043641  =    7.81995  —  10  =  log  0.0066062 

.-.  Vo.000043641  =  0.0066062. 


li 


(8)  Find  the  sixth  root  of  0.076553. 
Page  16.  log  0.076553 

Divide  by  6  (§  6), 


=   8.88397-10 
60  -50 


Page  13. 


^ 6)58.88397-60 

log  -^0.076553       =   9.81400 -10  =  log  0.66163 
.-.  VO.076553       =   0.66163. 


Exercises. 

Find  by  logarithms  the  value  of : 
45607  „     5.6123 


1. 


31046 


2. 


0.01987 


3. 


2.667 
0.06786 


xu 


LOGARITHMS. 


4. 


0.06547 


74.938  X  0.05938 


6. 


4.657  X  0.03467 
3.908  X  0.07189* 

0.0075389  X  0.0079 
0.00907  X  0  009784* 


7. 


8. 


9. 


312  X  7.18  X  31.82, 
619X8.27  X  5.132* 

0.007  X  57.83  X  28.13 
9.317  X  00.28  X  476.6* 

6.65  X  0.0007632  X  0.87654 
2.79  X  0.0009524  X  1.46785 


/0.00.S457  X  43l 
\  0.005824  X  15.' 


387  X  99.2  X  0.00026 


724  X  1.38  X  0.00089 


3/23: 


815  X  29.36  X  0.007  X  0.62487 
00072  X  9.236  X  5.924  X  3.0007 


/3.1416  X  0. 
\  1.7285  X  0. 


031416  X  0.0031416 


017285  X  0.0017286 


? 


I  i' 


TABLE  n. 

22.   This  table  (page  20)  contains  the  value  of  the  number  t, 
its  most  useful  combinations,  and  their  logarithms. 

Find  the  length  of  an  arc  of  47°  32'  57'*  in  a  unit  circle. 


47°  32'  57"  =  171177" 

log  171177      =  6.23344 

log  \                     =  4.68557  - 

-10 

log  arc  47°  32'  57"  =  9.91901  -  10  =  log  0.82994 
.-.  length  of  arc       =  0.82994. 

Find  the  angle  if  the  length  of  its  arc  in  a  unit  circle =0.54936. 


log  0.54936 


=  9.73986-10 


colog -7,  =  log  a"  =6.31443 


log  angle 
.-.  angle 


=  5.05429  =  log  113816 
=  113316"  =  31°  28'  36". 


11 1 


INTRODUCTION. 


ZIU 


23.   The  relations  between  arcs  and  angles  given  in  Table  IL 
are  readily  deduced  from  the  circular  measure  of  an  angle. 
In  Circnlar  Measure  an  angle  is  defined  by  the  equation 


arc 


angle  =  —- — , 
radius 

in  which  the  word  arc  denotes  the  length  of  the  arc  corresponding 
to  the  angle,  when  both  arc  and  radius  are  expressed  in  terms  of 
the  same  linear  unit. 

Since  the  arc  and  radius  for  a  given  angle  in  different  circles 
vary  in  the  same  ratio,  the  value  of  the  angle  given  by  this  equa- 
tion is  independent  of  the  value  of  the  radius.     . 

The  angle  which  is  measured  by  a  radius-arc  is  called  a  Radian, 
and  is  the  angular  unit  in  circular  measure. 

Since  (7  =  2  wR,  it  follows  that  -^—2'ir,  and  ^  =  tt.  Therefore, 


B 


B 


If  the  arc  =  circumference, 
If  the  arc  =  semicircumference, 
If  the  arc  =  quadrant, 
If  the  arc  =  radius, 

Therefore,  tt  =  180°,  ^  tt  =  90°,  J  tt  =  60°,  ^77  =  45°,  J  tt  =  30°, 
j^  TT  =  22J°,  and  so  on. 

Since  180°  in  common  measure  equals  tt  units  in  circular  measure, 


the  angle  =  2  tt. 
the  angle  =  tt. 
the  angle  =  ^  tt. 
the  angle  =  1. 


1°  in  common  measure 


IT 


=  Jq^  units  in  circular  measure ; 


180° 
1  unit  in  circular  measure  = in  common  measure. 


TT 


By  means  of  these  two  equations,  the  value  of  an  angle  expressed 

in  one  measure  may  be  changed  to  its  value  in  the  other  measure. 

Thus,  the  angle  whose  arc  is  equal  to  the  radius  is  an  angle  of 

180° 
1  unit  in  circular  measure,  and  is  equal  to  ,  or  57°  17'  45", 

very  nearly. 

TABLE  m. 

24.  This  table  (pp.  21-49)  contains  the  logarithms  of  the  trigo- 
nometric functions  of  angles.  In  order  to  avoid  negative  character- 
istics, the  characteristic  of  every  logarithm  is' printed  10  too  large. 
Therefore,  — 10  is  to  be  annexed  to  each  logarithm. 

On  pages  28-49  the  characteristic  remains  the  same  throughout 
each  column,  and  is  printed  at  the  top  and  the  bottom  of  the  column* 


^ 


I 


I 


XIV 


LOGARITHMS. 


i 


But  on  pp.  30,  49,  the  characteristic  changes  one  unit  in  value  at  the 
places  marked  with  bars.  Above  these  bars  the  proper  characteristic 
is  printed  at  the  top,  and  below  them  at  the  bottom,  of  the  column. 

25.  On  pages  28-49  the  log  sin,  log  tan,  log  cot,  and  log  cos,  of 
1°  to  89**,  are  given  to  every  minute.  Conversely,  this  part  of  the 
table  gives  the  value  of  the  angle  to  the  nearest  minute  when 
log  sin,  log  tan,  log  cot,  or  log  cos  is  known,  provided  log  sin  or 
log  cos  lies  between  8.24186  and  9.99993,  and  log  tan  or  log  cot 
lies  between  8.24192  and  11.75808. 

If  the  exact  value  of  the  given  logarithm  of  a  function  is  not 
found  in  the  table,  the  value  nearest  to  it  is  to  be  taken,  unless 
interpolation  is  employed  as  explained  in  §  26. 

If  the  angle  is  less  than  45°  the  number  of  degrees  is  printed  at 
the  top  of  the  page,  and  the  number  of  minutes  in  the  column  to 
the  left  of  the  columns  containing  the  logarithm.  If  the  angle 
is  greater  than  45°,  the  number  of  degrees  is  printed  at  the  bottom 
of  the  page,  and  the  number  of  minutes  in  the  column  to  the  right 
of  the  columns  containing  the  logarithms. 

If  the  angle  is  less  than  45°,  the  names  of  its  functions  are 
printed  at  the  top  of  the  page ;  if  greater  than  45°,  at  the  bottom 
of  the  page.     Thus, 

Page  38.    log  sm  21**  37' =    9.56631-10. 

Page  45.     log  cot  36°  53'  =  10.12473  -  10  =  0.1247a 

Page  37.     log  cos  69°  14' =    9.54969-10. 

Page  49.     log  tan  45°  59'  =  10.01491  -  10  =  0.01491. 

Page  48.     If  log  cos  =  9.87468  -  10,  angle  =  41°  28^. 

Page  34.     If  log  cot  =  9.39353  -  10,  angle  =  76°  6'. 

If  log  sin  =  9.47760  —  10,  the  nearest  log  sin  in  the  table  is  9.47774  —  10 
(page  36),  and  the  angle  corresponding  to  this  value  is  17°  29'. 

K  log  tan  =  0.76520  =  10.76520  -  10,  the  nearest  log  tan  in  the  table  is 
10.76490  — 10  (page  32),  and  the  angle  corresponding  to  this  value  is  80°  16'. 

26.  If  it  is  desired  to  obtain  the  logarithms  of  the  functions  of 
angles  that  contain  seconds,  or  to  obtain  the  value  of  the  angle  in 
degrees,  minutes,  and  seconds,  from  the  logarithms  of  its  functions, 
interpolation  must  be  employed.      Here  it  must  be  remembered 

that,  •       v        w 

The   difference  between  two   consecutive  angles  in  the  table 

is  60".  ,  - 

Log  sin  and  log  tan  increase  as  the  angle  increases ;  log  cos  and 

log  cot  diminish  as  the  angle  increases. 


INTBODUCTIOir. 


Find  log  tan  70*»  46'  8". 

Page  37.    log  tan  70°  46'  =  0.46731. 

The  difference  between  the  mantissas  of  log  tan  70®  46'  and  log  tan  70°  47' 
is  41,  and  ^  of  41  =  5. 

As  the  function  is  increasing,  the  6  must  be  added  to  the  figure  in  the  fifth 
place  of  the  mantissa  45731 ;  and 

Therefore  log  tan  70°  46'  8"  =  0.46736. 


m 


Find  log  cos  47°  35'  4". 

Page  48.    log  cos  47°  35' =  9.82899 -10. 

The  difference  between  this  mantissa  and  the  mantissas  of  the  next  log  cos 
is  14,  and  ^\  of  14  =  1. 

As  the  function  is  decreasing,  the  1  must  be  subtracted  from  the  figure  in  the 
fifth  place  of  the  mantissa  82899 ;  and 

Therefore  log  cos  47°  36'  4"  =  9.82898  -  10. 


Find  the  angle  for  which  log  sin  =  9.45369  — 10. 

Page  35.    The  mantissa  of  the  nearest  smaller  log  sin  in  the  table  is  45334. 

The  angle  corresponding  to  this  value  is  16°  30'. 

The  difference  between  45334  and  the  given  mantissa,  45359,  is  25. 

The  difference  between  45334  and  the  next  following  mantissa,  45377,  is  43, 
and  If  of  60"  =35". 

As  the  function  is  increasing,  the  35"  must  be  added  to  16°  30'j  and  the 
required  angle  is  16°  30'  36". 


»' 


Find  the  angle  for  which  log  cot =0.73478. 

Page  32.    The  mantissa  of  the  nearest  smaller  log  cot  in  the  table  is  73415. 

The  angle  corresponding  to  this  value  is  10°  27'. 

The  difference  between  73415  and  the  given  mantissa  is  63. 

The  difference  between  73415  and  the  next  following  mantissa  is  71,  and  ^ 
of  60"  =  53". 

As  the  function  is  decreasmg,  the  63"  must  be  subtracted  from  10°  27';  and 
the  required  angle  is  10°  26'  7". 


Find 


Exercises. 

1. 

logshi36o  8'  9^. 

9. 

log  tfl.Ti  25°  27'  47^ 

2. 

log  sin  54°  54' 40^. 

10. 

log  cos  56°  11'  67". 

3. 

log  cos  43°  32' 31". 

11. 

log  cot  62°  0'   4". 

4. 

log  cos  69°  26' 11". 

12. 

log  cos  75°  26' 58". 

6. 

logta.n32°   9' 17". 

13. 

log  Un  33°  27'  13". 

6. 

logUn50°   2'   2". 

14. 

log  cot  81°  55'  24". 

7. 

log  cot  44°  33'  17". 

16. 

log  tan  89°  46' 36". 

8. 

log  cot  55°   9' 32". 

16. 

log  tan   1°25'66". 

I 


f 


* 


XVI 


L0GABITH9CS. 


Find  the  angle  A  if 


17. 

log  sin  -4  = 

9.70075. 

25. 

log  cos  A  = 

9.40008. 

18. 

log  sin  ^  = 

9.91289. 

26. 

log  cot  A  = 

9.78815. 

19. 

log  cos  A  = 

9.86026. 

27. 

log  cos  A  = 

9.34301. 

20. 

log  cos  A  = 

9.54595. 

28. 

log  tan  A  = 

10.52288. 

21. 

log  tan  ^  = 

9.79840. 

29. 

log  cot  A  = 

965349. 

22. 

log  tan  4  = 

10.07671. 

30. 

log  sin  -4  = 

8.39316. 

23. 

log  cot  A  = 

10.00675. 

31. 

log  sin  ^  = 

8.06676. 

24. 

log  cot  A  = 

9.84266. 

32. 

log  tan  A  = 

8.11148. 

27.    If  log  sec  or  log  esc  of  an  angle  is  desired,  it  may  be  found 
from  the  table  by  the  formulas, 

;  hence,  log  sec  A  =  colog  cos  A. 


sec -4  = 
csc^  = 


cos^ 
1 

sin -4 


;  hence,  log  esc  A  =  colog  sin  A. 


Page  31.     log  sec    8°  28'        =  colog  cos   8°  28'        =0.00476. 
Page  42.     log  esc  59°  36'  44"  =  colog  sin  59°  36'  44"  =  0.06418. 

28.  If  a  given  angle  is  between  0°  and  1°,  or  between  89°  and  90**; 
or,  conversely,  if  a  given  log  sin  or  log  cos  does  not  lie  between  the 
limits  8.24186  and  9.99993  in  the  table;  or,  if  a  given  log  tan  or 
log  cot  does  not  lie  between  the  limits  8.24192  and  11.75808  in  the 
table ;  then  pages  21-24  of  Table  III.  must  be  used. 

On  page  21,  log  sin  of  angles  between  0°  and  0°  3',  or  log  cos  of 
the  complementary  angles  between  89°  57'  and  90°,  are  given  to 
every  second;  for  the  angles  between  0°  and  0°  3',  log  tan  ^ log  sin, 
and  log  cos  =  0.00000 ;  for  the  angles  between  89°  57'  and  90°, 
log  cot  =  log  cos,  and  log  sin  =  0.00000. 

On  pages  22-24,  log  sin,  log  tan,  and  log  cos  of  angles  between 
0°  and  1°,  or  log  cos,  log  cot,  and  log  sin  of  the  complementary 
angles  between  89°  and  90°,  are  given  to  every  10". 

Whenever  log  tan  or  log  cot  is  not  given,  they  may  be  found  by 
the  formulas, 

log  tan  =  colog  cot.  log  cot  =  colog  tan. 

Conversely,  if  a  given  log  tan  or  log  cot  is  not  contained  in  the 
table,  then  the  colog  must  be  found ;  this  will  be  the  log  cot  or 
log  tan,  as  the  case  may  be,  and  will  be  contained  in  the  table. 

On  pages  25-27  the  logarithms  of  the  functions  of  angles 
between  1°  and  2°,  or  between  88°  and  90°,  are  given  in  the  manner 
employed  on  pages  22-24.  These  pages  should  be  used  if  the  angle 
lies  between  these  limits,  and  if  not  only  degrees  and  minutes,  but 
degrees,  minutes,  and  multiples  of  10"  are  given  or  required. 


INTRODUCTION. 


xvu 


When  the  angle  is  between  0°  and  2°,  or  88°  and  90°,  and  a 
greater  degree  of  accuracy  is  desired  than  that  given  by  the  table, 
interpolation  may  be  employed ;  but  for  these  angles  interpolation 
does  not  always  give  true  results,  and  it  is  better  to  use  Table  IV. 


Find  log  tan  0°  2'  47",  and  log  cos  89°  37'  20". 
Page  21.  log  tan  0°  2' 47"  =  log  sin  0°  2' 47 
Page  23.      log  cos  89°  37'  20"  =  7.81911  -  10. 


"  =  6.90829-10. 


Find  log  cot  0°  2'  15".. 


Page  21.      log  tan  0°  2'  15 
Therefore,  log  cot  0°  2'  15 


// 


10  -10 

=    6.81591-10 


."     =    3.18409 


Find  log  tan  89°  38'  30". 

10-10 

Page  23.      log  cot  89°  38'  30"  =    7.79617  -  10 
Therefore,  log  tan  89°  38' 30"  =    2.20383 

Find  the  angle  for  which  log  tan  =  6.92090  — 10. 
Page  21.     The  nearest  log  tan  is  6.92110  —  10. 
The  corresponding  angle  for  which  is  0°  2'  52". 

Find  the  angle  for  which  log  cos  =  7.70240  — 10. 
Page  22.     The  nearest  log  cos  is  7.70261  —  10. 
ITie  corresponding  angle  for  which  is  89°  42'  40". 

Find  the  angle  for  which  log  cot  =  2.37368. 

This  log  cot  is  not  contained  in  the  table. 
The  colog  cot  =  7.62632  —  10  =  log  tan. 

The  log  tan  in  the  table  nearest  lo  this  is  (page  22)  7.62510 
angle  corresponding  to  this  value  of  log  tan  is  0°  14'  30". 


10,  and  the 


29.   If  an  angle  x  is  between  90°  and  360°,  it  foUows,  from 
formulas  established  in  Trigonometry,  that, 

between  180°  and  270°, 


between  90°  and  180°, 
log  sin  X  =  log  sin  (180°  —  a;), 
log  cos  X  =  log  cos  (180°  —  x) 
log  tan  X  =  log  tan  (180°  —  x) 
log  cot  X  =  log  cot  (180°  —  x\ ; 

between  270°  and  360°, 
log  sin  X  =  log  sin  (360°  —  x)^ 
log  cos  X  =  log  cos  (360°  —  x), 
log  tan  X  =  log  tan  (360°  —  x)^ 
log  cot  X  =  log  cot  (360°  —  x\. 


nt 


log  sin  a;  =  log  sin  (x  — 180°) 
log  cos  X  =  log  cos  (x  — 180°)  „, 
log  tan  X  =  log  tan  (x  — 180°), 
log  cot  ic  =  log  cot  (ic  — 180°)j 


f 


1 1 


\ 


!   ! 


XVlll 


LOGARITHMS. 


The  letter  n  is  placed  (according  to  custom)  after  the  logarithms 
of  those  functions  which  are  negative  in  value. 

The  above  formulas  show,  without  further  explanation,  how  to 
find  by  means  of  Table  III.  the  logarithms  of  the  functions  of  any 
angle  between  90°  and  360°. 

Thus,  log  sin  137°  45'  22"  =  log  sin  42°  14'  38"  =  9.82756  -  10. 
log  cos  137°  46'  22"  =  log„  cos  42°  14'  38"  =  9.86940„  -  10. 
log  tan  137°  45'  22"  =  log„  tan  42°  14'  38"  =  9.95815„  -  10. 
log  cot  137°  45'  22"  =  log„  cot  42°  14'  38"  =  0.04185„. 
log  sin  209°  32'  50"  =  log„  sin  29°  32'  50"  =  9.69297„  -  10. 
log  cos  330°  27'  10"  =  log  cos   29°  32'  50"  =  9.93949  —  10. 

Conversely,  to  a  given  logarithm  of  a  trigonometric  function 
there  correspond  between  0°  and  360°  four  angles,  one  angle  in 
each  quadrant,  and  so  related  that  if  x  denote  the  acute  angle,  the 
other  three  angles  are  180°  —a;,  180°  +x,  and  360°  —x. 

If  besides  the  given  logarithm  it  is  known  whether  the  function 
is  positive  or  negative,  the  ambiguity  is  confined  to  two  quadrants, 
therefore  to  two  angles. 

Thus,  if  the  log  tan  =  9.47451  -  10,  the  angles  are  16°  36'  17"  in  Quadrant  I. 
and  196°  36'  17"  in  Quadrant  III. ;  but  if  the  log  tan  =  9.47451„-  10,  the  angles 
are  163°  23'  43"  in  Quadrant  II.  and  343°  23'  43"  m  Quadrant  IV. 

To  remove  all  ambiguity,  further  conditions  are  required,  or  a 
knowledge  of  the  special  circumstances  connected  with  the  problem 
in  question. 

TABLE  IV. 

30.  This  table  (page  50)  must  be  used  when  great  accuracy  is 
desired  in  working  with  angles  between  0°  and  2°,  or  between  88° 
and  90°. 

The  values  of  S  and  T  are  such  that  when  the  angle  a  is 
expressed  in  seconds, 

S  =  log  sin  a  —  log  a", 
T  =  log  tan  a  —  log  a". 

Hence  follow  the  formulas  given  on  page  50. 

The  values  of  S  and  T  are  printed  with  the  characteristic  10  too 
large,  and  in  using  them  — 10  must  always  be  annexed. 


Find  log  sin  0°  58'  17". 

0°  58'  17"  =  3497" 
log  3497  =  3.54370 

S  =  4.68555  —  10 
log  sin  0°  58'  17"  =  8.22925  —  10 


Find  log  cos  88°  26'  41.2". 

90°  -  88°  26'  41.2"  =  1°  33'  18.8" 

=  5598.8" 
log  5698.8  =  3.74809 

S  =  4.68552  -  10 
log  cos  880  26'  41.2"  =  8.43361  —  10 


f 


INTRODUCTION. 


XIX 


Find  log  tan  0°  52'  47.5". 

0°  52'  47.5"  =  3167.5" 
log  3167.5  =  3.50072 

T  ==  4.68561  —  10 
log  tan  0°  52'  47.5"  =  8.18633  -  10 


Find  log  tan  89°  54'  37.362". 

90°  -  89°  54'  37.362"  =  0°  5'  22.638" 

=  322.638" 
log  322.638  =  2.50871 

T  =  4.68558  —  10 
log  cot  89°  54'  37.362"  =  7.19429  -  10 
log  tan  89°  54'  37.362"  =  2.80571 


Find  the  angle,  if  log  sin  =  6.72306 -10. 

6.72306  - 10 
S  =  4.68557  -  10 
Subtract,     2.03749  =  log  109.015 

109.015"        =  0°  1'  49.016". 

Find  the  angle  for  which  log  cot  =  1.67604. 

colog  cot  =  8.32396  -  10 
T  =  4.68564  —  10 
Subtract,     3.63832  =  log  4348.3 

4348.3"  =  1°  12'  28.3". 

Find  the  angle  for  which  log  tan  =  1.55407. 

colog  tan  =  8.44593  —  10 
T  =  4.68569 -10 
Subtract,     3.76024  =  log  5767.6 

6757.6"  =  1°  35'  57.6", 

and      90°  -  1°  35'  57.6"  =  88°  24'  2.4". 


Therefore,  the  angle  required  is  88°  24'  2.4". 

TABLE  V. 

31.  This  table  (p.  51),  containing  the  circumferences  and  areas 
of  circles,  does  not  require  explanation. 

TABLE  VI. 

32.  Table  VI.  (pp.  52-69)  contains  the  natural  sines,  cosines, 
tangents,  and  cotangents  of  angles  from  0°  to  90°,  at  inter- 
vals of  1'.  If  greater  accuracy  is  desired  it  may  be  obtained 
by  interpolation. 

Note.  In  preparing  the  preceding  explanations,  we  have  made  free  use 
of  the  Logarithmic  Tables  by  F.  G.  Gauss.  For  Table  VI.  we  are  indebted 
to  D.  Carhart. 

TABLE  Vn. 

33.  This  table  (pp.  70-75)  gives  the  latitude  and  departure  to 
three  places  of  decimals  for  distances  from  1  to  10,  corresponding 
to  bearings  from  0°  to  90°  at  intervals  of  15'. 


il 


LOGARITHMS. 


If  the  bearing  does  not  exceed  45°  it  is  found  in  the  lefi-hand 
column,  and  the  designations  of  the  columns  under  "Distance" 
are  taken  from  the  top  of  the  page;  but  if  the  bearing  exceeds 
45°,  it  is  found  in  the  W^^^hand  column,  and  the  designations 
of  the  columns  under  "Distance"  are  taken  from  the  bottom  of 
the  page. 

The  method  of  using  the  table  will  be  made  plain  by  the  follow- 
ing examples :  — 


(1)   Let  it  be  required  to  find  the  latitude  and  departure  of  the 
course  K  35°  15'  E.  6  chains. 


til 


On  p.  75,  left-hand  column,  look  for  35**  15' ;  opposite  this  bearing,  in  the 
vertical  column  headed  "Distance  6,"  are  found  4.900  and  3.463  under  the 
headings  "Latitude"  and  "Departure"  respectively.  Hence,  latitude  or 
northing  =  4.900  chains,  and  departure  or  easting  =  3.463  chains. 

(2)  Let  it  be  required  to  find  the  latitude  and  departure  of  the 
course  S.  87°  W.  2  chains. 

As  the  bearing  exceeds  45°,  we  look  in  the  right-hand  column  of  p.  70,  and 
opposite  87°  in  the  column  marked  "  Distance  2  "  we  find  (taking  the  designa- 
tions of  the  columns  from  the  bottom  of  the  page)  latitude  =  0.105  chains,  aud 
departure  =  1.997  chains.  Hence,  latitude  or  southing  =  0. 105  chains,  and 
departure  or  westing  =  1.997  chains. 

(3)  Let  it  be  required  to  find  the  latitude  and  departure  of  the 
course  K  15°  45'  W.  27.36  chains. 


\l 


In  this  case  we  find  the  required  numbers  for  each  figure  of  the  distance 
separately,  arranging  the  work  as  in  the  following  table.  In  practice,  only  the 
last  columns  under  *'  Latitude  "  and  *'  Departure  "  are  written. 


M^- 


DiSTAKCS. 

Latitude. 

Departube. 

20      =  2  X  10       ' 
7 

0.3   =3-7-10 
0.06  =  6  -r  100 

1.925  X  10    =  19.25 

6.737 

2.887  4-10    =0.289 

6.775  -r  100  =  0.058 

0.543  X  10    =  6.43 
L90 
0.814 -r  10    =0.081 
1.628  -f  100  =  0.016 

27.36 

26.334 

7.427 

Hence,  latitude  =  26.334  chains,  and  departure  =  7.427  chains. 


■\ 

TABLE  I 

THE 

COMMON  OE  BEIGGS  LOGAEITHMS 

OP  THE 

• 

NATUEAL  :S  UMBEES 

From  1  to  10000. 

1-100 

N 

log 

N 

log 

N           log 

N 

log 

N          log 

1 

0.00  000 

21 

1.32  222 

41     1.  61  278 

61 

1.  78  533 

81     1.90  849 

2 

0.30103 

22 

1.  34  242 

42     1.62  325 

62 

1.79  239 

82     1.  91 381 

3 

a  47  712 

23 

1.  36  173 

43     1.  63  347 

63 

1.79  934 

83     1.  91  908 

4 

0.60  206 

24 

1.  38  021 

44     1.  64  345 

64 

1.80  618 

84    1.92  428 

5 

0.69  897 

25 

1.39  794 

45     1.65  321 

65 

1.81291 

85     1.92  942 

6 

0.77  815 

26 

1.  41  497 

46    1.66  276 

66 

1.  81  954 

86    1.93  4iO 

7 

0.  84  510 

27 

1.  43  136 

47    1.67  210 

67 

1.  82  607 

87    1.93  952 

8 

0.90309 

28 

1.  44  716 

48     1.68124 

68 

1.  83  251 

88    1.94  448 

9 

0.  95  424 

29 

1.46  240 

49     1.69  020 

69 

1.  83  885 

89     1.94  939 

10 

1.00000 
'  1 

30 

1.  47  712 

50     1.69  897 

70 

1.  84  510 

• 

90    1.95  424 

11 

1.04139 

31 

1.  49  136 

61     1.  70  757 

71 

1.  85  126 

91     1.95  904 

12 

1.07918 

32 

1.50  515 

52     1.71600 

72 

1.  85  733 

92     l.%379 

13 

1.11394 

33 

1.  51  851 

53     1.72  428 

73 

1.86332 

93     1.  %848 

14 

1.14  613 

34 

1.  53  148 

54     1.  73  239 

74 

1.86  923 

94    1.97  313 

15 

1.17  609 

35 

1.54  407 

55     1.74  036 

75 

1.  87  506 

95     1.  97  772 

16 

1.20412 

36 

1.  55  630 

66    1.74  819 

76 

1.88  081 

96    1.98  227 

17 

1.  23  045 

37 

1.56  820 

57    1.75  587 

77 

1.88  649 

97     1.98677 

18 

1.  25  527 

38 

1.57  978 

58     1.76  343 

78 

1.  89  209 

98    1.99123 

19 

1.27  875 

39 

1.  59  106 

59    1.  77  085 

79 

1.  89  763 

99     1. 99  564 

20 

1.  30  103 

40 

1.60  206 

60    1.77  815 

80 

1.90309 

100    2.00000 

N 

log 

N 

log 

N         log 

N 

log 

N         log 

1-100 


V 


ti 


I 


V 


2 


100-160 


\ 


!  i 


i 


N 

O          1         2         3         4 

5         6          7          8         9 

lOO 

00000  00(H3  00087  00130  00173 

00217  00260  00303   00346  00389 

101 

00432  00  475   00  518  00  561  00  604 

00647  00689  00732  00775  00817 

102 

00860  00903  00945  00988  01030 

01  072  01 115  01 157  01 199  01  242 

103 

01284  01326  01368  01410  01452 

01494  01536  01578  01620  01662 

104 

01703  01745   01787  01828  01870 

01912  01953  01995  02  036  02  078 

105 

02119  02160  02  202  02  243  02  284 

02325   02  366  02  407  02  449  02  490 

106 

02  531  02  572  02  612  02  653  02  694 

02  735   02  776  02  816  02  857  02  898 

107 

02  938  02  979  03  019  03  060  03100 

03141   03181   03  222  03  262  03  303 

108 

03  342  03  383  03  423   03  463  03  503 

03  543   03  583   03  623  03  663   03  703 

109 

03  743  03  782  03  822  03  862  03  902 

03  SHI  03  981  04  021  0+060  04100 

no 

(H 139  04  179  04  218  (H  258  04  297 

0+336   0+376  0+415  04  454  0+493 

111 

(H532  0+571   0+610  0+650  0+689 

0+727  0+766  04  805  0+-844  04  883 

112 

0+922  0+%l  0+999  05  038  05  077 

05  115  05  154  05  192  05  231  05  269 

113 

05  308  05  346  05  385   05  423  05  461 

05  500  05  538  05  576  05  614  05  652 

114 

05  690  05  729  05  767  05  805  05  843 

05  881   05  918  05  956  05  994  06032 

116 

06070  06108  06145  06183  06  221 

06258  06  296  06333  06  371  06408 

116 

06446  06483  06  521   06  558  06  595 

06633   06670  06  707  06  7+4  06  781 

117 

06819  06  856  06893  06  930  06  %7 

0700+  070+1   07078  07115  07151 

118 

07188  07  225   07  262   07  298  07  335 

07  372  07  408  07  445  07  482  07  518 

119 

07  55i  07  591  07  628  07  66+  07  700 

07  737  07  773  07  809  07  846  07  882 

120 

,07918  07954  07990  08027  08063 

08099  08135  08171  08  207  08  243 

121 

08  279  08  314  08  350  08  386  08422 

08  458  08493  08  529  08  565   08600 

122 

08  636  08  672  08  707  08  743  08  778 

08  814  088+9  08  884  08920  08955 

123 

08991   09026  09061   090%  09132 

09167  09  202   09  237   09  272  09307 

124 

09342  09377  09412  09  447  09  482 

09  517  09  552  09  587  09621   09656 

125 

09691  09  726  09  760  09  795  09  830 

09  864  09899  09934  09968   10003 

126 

10037   10072   10106   10140   10175 

10  209   10  2+3   JO  278   10312   10  3+6 

127 

10380  10  415    10449   10  483   10  517 

10  551   10  585   10619  10653   10687 

128 

10  721   10  755   10  789  10823   10  857 

10890  10  924   10958   10992   11025 

129 

11059  11093   11126   11160   11193 

11227   11261   11294   11327   11361 

130 

11394  11428   11461   1149+  11528 

11561   11594  11628  11661   11694 

131 

11727   11760   11793   11826  11860 

11893   11926  11959  11992   12  024' 

132 

12  057   12  090   12123   12156  12189 

12  222   12  254   12  287   12  320  12  352 

133 

12  385   12  418   12  450  12  483   12  516 

12  548  12  581   12  613   12  646  12  678 

134 

12  710  12  743   12  775   12  808   12  840 

12872   12  905   12  937  12  %9  13  001 

• 

135 

13033   13  066   13  098   13130  13162 

13194   13  226  13  258  13  290  13  322 

136 

13  354   13  386   13  418   13  450   13  481 

13  513   13  545   13  577  13  609  13  640 

137 

13  672   13  70+   13  735   13  767   13  799 

13  830  13  862   13  893  13  925   13  956 

138 

13  988   14  019   14  051    14  082   14114 

14145   14176  14  208   14  239  14  270 

139 

14  301   14  333   14  364   14  395   14  426 

14  457   14  489  14  520  14  551   14  582 

140 

14  613   14  644   14  675   14  70^  14  737 

14  768   14  799  14  829  14  860  14  891 

141 

14922  14  953   14  983   15  014  15  0+5 

15  076   15  106   15  137   15  168  15198 

142 

15  229  15  259  15  290  15  320  15  351 

15  381   15  412   15  442   15  473   15  503 

143 

15  534  15  564  15  594   15  625   15  655 

15  685   15  715   15  746  15  776  15  806 

144 

15  836  15  866   15  897   15  927  15  957 

15  987  16017  16047  16077  16107 

145 

16137  16167  16197  16  227  16256 

16286  16316  16346  16376  16406 

146 

16435   16465   16495   16  524  16  554 

16  584   16613   16643   16673   16  702 

147 

16  732   16  761   16  791   16  820  16  850 

16879  16909   16  938   16  %7   16  997 

148 

17  026  17  056  17085   17114  17143 

17173   17  202  17  231   17  260  17  289 

1 

149 

17  319  17  348  17377   17  406  17435 

17464  17  493   17  522  17  551   17  580 

150 

17609  17638  17667  1769j5  17725 

17  754  17  782  17811  17840  17869 

N 

O     ^  1         Z        3        4 

5         6         7         8         9 

1 

100-1^ 

50 

i  , 

160-200                              8 

N 

O        1        a        3        4 

5         6          7          8         9 

150 

17  609  17  638  17  6(^7   17  6%   17  725 

17  754  17  782  17  811   17  8+0  17  869 

151 

17  898   17  926   17  955    17  98+   18  013 

18  041   18  070  18  099   18127   18156 

152 

18184   18  213   18  2+1   18  270   18  298 

18  327   18  355   18384   18  412   18  441 

153 

18  469  18498  18  526  18  554  18  583 

18  611   18  639  18667  18  6%  18  724 

154 

18  752   18  780   18  808   18  837   18  865 

18  893   18921   18  949   18  977   19005 

155 

19033   19061   19  089  19117   19145 

19173   19  201   19  229  19  257  19  285 

156, 

19  312  19  340   19  368   19  396   19  424 

19  451   19  479   19  507   19  535   19  562 

157 

19  590   19  618   19  645    19  673   19  700 

19  728   19  756.19  783   19  811   19  838 

158 

19  866   19  893   19  921   19  9+8   19  976 

20  003   20  030  20  058  20085   20112 

159 

201+0  20167  2019+  20  222  20  249 

20  276  20303  20  330  20  358  20385 

160 

20  412  20  439  20466  20  493   20  520 

20  548  20  575   20  602  20  629  20  656 

161 

20  683   20  710  20  737   20  763   20  790 

20S17   20  84+  20  871   20  898  20  925 

162 

20  952'  20  978  21  005   21  032  21  059- 

21085   21112   21139  21165   21192 

163 

21219  212+5   21272   21299  21325 

21352  21378  21405   21431   21458 

164 

21484  21511   21537   21564  21590 

21  617  21  643   21  669  21  6%  21  722 

165 

21748  21775   21801   21827  21854 

21880  21906  21932  21 958  21985 

166 

22  011   22  037  22  063   22  089  22  115 

22  1+1   22167   22  194  22  220  22  246 

167 

22  272  22  298"  22  324  22  350  22  376 

22  401   22  427   22  453   22  479  22  505 

168 

22  531   22  557   22  583   22  608  22  63+ 

22  660  22  686  22  712   22  737   22  763 

169 

22  789  22  814   22  8+0  22  866  22  891 

22  917  22  9+3   22  968  22  99+  23  019 

170 

23  0^5   23  070  23  096  23  121   23  1+7 

23172  23198  23  223  23  2+9  23  27+ 

171 

23  300  23  325   23  350  23  376  23  401 

23  426  23  452  23  477  23  502   23  528 

172 

23  553   23  578  23  603   23  629  23  65+ 

23  679  23  704  23  729  23  75+  23  779 

173 

23  805   23  830  23  855   23  880  23  905 

23  930  23  955   23  980  24  005   24  030 

17+ 

2+055   2+080  2+105   2+130  2+155 

24180  24  20+  24  229  24  254  24  279 

175 

2430+  2+329  24  353  24  378  24  403 

24  428  24  452  24477   24  502   24  527 

176 

24  551   2+576  2+601   2+625   24  650 

24  674  24  699  24  724   24  748  24  773 

177 

24  797   2+822   24  8+6  2+871   24  895 

24  920  24  944  24  969  24  993  25  018 

178 

25  0+2   25  066  25  091   25  115   25  139 

25  16+  25  188   25  212   25  237   25  261 

179 

25  285   25  310  25  334  25  358  25  382 

25  406  25  431   25  455   25  479  25  503 

ISO 

25  527  25  551   25  575'  25  600  25  62+ 

25  648  25  672  25  6%  25  720  25  744 

181 

25  768  25  792  25  816  25  8+0  25  864  ' 

25  888  25  912  25  935   25  959  25  983 

182 

26007   26  031   26055   26  079  26102 

26126  26150  26174   26198  26  221 

183 

26  2+5   26  269  26  293   26316  26  3+0 

26  36+  26  387   26  411   26  435   26458 

184 

26  482  26  505   26  529  26  553   26  576 

26  600  26623   26  647  26  670  26  694 

185 

26  717  26  7+1   26  764  26  788  26  811 

26  834  26  858  26  881   26905   26  928 

186 

26  951   26  975   26  998  27  021   27  045 

27  068  27  091   27114  27138  27161 

187 

27184  27  207   27  231   27  254  27  277 

27  300  27  323   27  346  27  370  27  393 

188 

27  416  27  439  27  462   27  485   27  508 

27  531   27  554  27  577  27  600  27  623 

189 

27  646  27  669  27692  27  715   27  738 

27  761  27  784  27  807  27  830  27  852 

190 

27  875   27  898  27  921  27  944  27967 

27  989  28  012  28  035  28  058  28081 

191 

28103   28126  281+9  28171   28194 

28  217   28  2+0  28  262  28  285   28  307 

192 

28330  28353   28375   28  398  28  421 

28  443   28466  28  488  28  511   28  533 

193 

28  556  28  578  28601   28  623   28  646 

28  668  28  691   28  713   28  735   28  758 

194 

28  780  28  803   28  825   28  847   28  870 

28  892  28914  28937  28  959  28  9^1 

195 

29  003   29026  290+8  29  070  29  092 

29115   29137  29159  29181   29  203 

196 

29  226  29  248  29  270  29  292  29  314 

29  336  29  358  29  380  29  403   29  425 

197 

29  447   29469  29  491   29  513   29  535 

29  557  29  579  29  601   29  623   29645 

198 

29  667  29  688  29  710  29  732  29  754 

29  776  29  798  29  820  29  842   29  863 

199 

29  885   29907   29  929  29  951   29  973 

29  994  30016  30038  30  060  30081 

200 

30103  30125  30146  30168  30190 

30  211  30  233  30  255  30  276  30  298 

N 

O         1          2         3         4 

5         6         7         8         9 

150-200 

M 


rtotiTi 


^:htm 


200-250 


I 


N 

O    1    2    3    4 

5    6    7    8    9 

200 

30103  30125  30146  30168  30190 

30  211  30  233  30  255  30  276  30  298 

201 

30320  30  341  30363  30  384  30  406 

30428  30449  30471  30  492  30  514 

202 

30  535  30  557  30  578  30  600  30  621 

30643  :0664  30685  30  707  30  728 

203 

30  750  30  771  30  792  30  814  30835 

30  856  30  878  30  899  30920  30  942 

2(n 

30963  30984  31006  31027  31048 

31069  31091  31112  31133  31154 

205 

31 175  31 197  31  218  31  239  31  260 

31281  31302  31323  31345  31366 

206 

31387  31408  31429  31450  31471 

31492  31513  31534  31555  31576 

207 

31597  31618  31639  31660  31681 

31702  31723  31744  31765  31785 

208 

31806  31827  31848  31869  31890 

31911  31931  31952  31973  31994 

209 

32  015  32  035  32  056  32  077  32  098 

32118  32139  32160  32181  32  201 

210 

32  222  32  243  32  263  32  284  32  305 

32  325  32  346  32  366  32  387  32  408 

211 

32  428  32  449  32  469  32  490  32  510 

32  531  32  552  32  572  32  593  32  613 

212 

32  634  32  654  32  675  32  695  32  715 

32  736  32  756  32  777  32  797  32  818 

213 

32  838  32  858  32  879  32  899  32  919 

32  940  32  960  32  980  33  001  33  021 

214 

33  (HI  33  062  33  082  33102  33122 

33  143  33163  33183  33  203  33  224 

215 

33  244  33  264  33  284  33  304  33  325 

33  345  33  365  33  385  33  405  33  425 

216 

33  445  33  465  33  486  33  506  33  526 

33  546  33  566  33  586  33  606  33  626 

217 

33  646  33  666  33  686  33  706  33  726 

33  746  33  766  33  786  33  806  33  826 

218 

33  846  33  866  33  885  33  905  33  925 

33  945  33  %5  33  985  34  005  34  025 

219 

34  (H4  34  064  34084  34104  34124 

34143  34163  34183  34  203  34  223 

220 

34  242  34  262  34  282  34  301  34  321 

34  341  34  361  34  380  34  400  34  420 

221 

34  439  34  459  34  479  34  498  34  518 

34  537  34  557  34  577  34  596  34  616 

222 

34  635  34  655  34  674  34  694  34  713 

34  733  34  753  34  772  34  792  34  811 

223 

34  830  34  850  34  869  34  889  34  908 

34928  34947  34  967  34  986  35  005 

224 

35  025  35  (H4  35  064  35  083  35  102 

35  122  35  141  35  160  35  180  35  199 

j^25 

*226 

35  218  35  238  35  257  35  276  35  295 

35  315  35  334  35  353  35  372  35  392 

35  411  35  430  35  449  35  468  35  488 

35  507  35-526  35  545  35  564  35  583 

227 

35  603  35  622  35  641  35  660  35  679 

35  698  35  717  35  736  35  755  35  774 

228 

35  793  35  813  35  832  35  851  35  870 

35  889  35  908  35  927  35  946  35  965 

229 

35  984  36003  36021  36  (HO  36059 

36078  36097  36116  36135  36154 

230 

36173  36192  36  211  36  229  36248 

36267  36  286  36305  36324  36342 

231 

36361  36380  36399  36418  36436 

36455  36474  36493  36  511  36  530 

232 

36  549  36S68  36  586  36605  36  624 

36642  36661  36  680  36  698  36  717 

233 

36  736  36  754  36  773  36  791  36810 

36  829  36847  36866  36  884  36903 

234 

36  922  36940  36959  36977  369% 

37014  37033  37051  37070  37  088 

235 

37107  37125  37144  37162  37181 

37199  37  218  37  236  37  254  37  273 

236 

37  291  37  310  37  328  37  346  37  365 

37  383  37  401  37  420  37  438  37  457 

237 

37  475  37  493  37  511  37  530  37  548 

37  566  37  585  37603  37621  37  639 

238 

37  658  37  676  37  694  37  712  37  731 

37  749  37  767  37  785  37  803  37  822 

239 

37  840  37  858  37  876  37  894  37912 

37931  37  949  37  %7  37  985  38003 

240 

38021  38039  38057  38075  38093 

38112  38130  38148  38166  38184 

241 

38  202  38  220  38  238  38  256  38  274 

38  292  38  310  38  328  38346  38  364 

242 

38  382  38399  38  417  38  435  38453 

38471  38  489  38  507  38  525  38  543 

243 

38561  38  578  38  5%  38  614  38632 

38650  38  668  38686  38  703  38  721 

244 

38  739  38  757  38  775  38  792  38810 

38828  38  846  38863  38881  38  899 

245 

38917  38  934  38952  38970  38987 

39005  39023  39041  39058  39076 

246 

39094  39111  39129  39146  39164 

39182  39199  39  217  39  235  39  252 

247 

39  270  39  287  39  305  39  322  39  340 

39358  39  375  39  393  39410  39428 

248 

39445  39  463  39  480  39498  39  515 

39  533  39  550  39  568  39  585  39  602 

249 

39620  39637  39  655  39  672  39690 

39  707  39  724  39  742  39  759  39  777 

250 

39  794  39  811  39  829  39  846  39  863 

39  881  39  898  39915  39933  39950 

N 

O    1    2    3    4 

6    6    7    8    9 

200-250 


Ai 


250-300 


5 


N 


250 

251 
252 
253 
254 

255 

256 

257 
258 
259 

260 

261 
262 
263 
264 

265 

266 
267 
268 
269 

270 

271 

272 
273 
274 

275 

276 

277 
278 
279 

280 

281 
282 
283 
284 

285 

286 
287 
288 
289 

290 

291 
292 
293 
294 

295 

2% 
297 
298 
299 

300 


O 


39  794 

39  967 
40140 

40  312 
40  483 

40654 
40  824 
40993 
41162 
41330 

41497 
41664 
41830 
41996 
42  160 

42  325 
42  488 
42  651 
42  813 
42  975 


39  811 

39  985 
40157 
40329 

40  500 

40  671 
40  841 
41010 
41179 
41347 

41514 
41681 
41847 
42  012 
42177 

42  341 
42  504 
42  667 
42  830 
42  991 


43  136  43  152 

43  297  43  313 

43  457  43  473 

43  616  43  632 

43  775  43  791 


43  933 
44091 

44  248 
44  404 
44  560 

44  716 

44  871 

45  025 
45  179 
45  332 

45  484 
45  637 
45  788 

45  939 
46090 

46  240 
46  389 

46  538 
46687 
46835 

46982 
47129 

47  276 
47  422 
47  567 


43  949 
44107 

44  264 
44  420 
44  576 

44  731 

44  886 

45  040 
45  194 
45  347 

45  500 
45  652 
45  803 

45  954 
46105 

46  255 
46404 
46  553 
46  702 
46  850 

46  997 
47144 

47  290 
47  436 

47  582 


39  829 
40002 
40175 

40  346 
40  518 

40688 
40  858 
41027 
41 .196 
41363 

41531 
41697 
41863 
42  029 
42193 

42  357 
42  521 
42  684 

42  846 

43  008 

43169 
43  329 
43  489 
^3  648 

43  807 

43  965 
44122 

44  279 
44  436 
44  592 

44  747 

44  902 

45  056 
45  209 
45  362 

45  515 
45  667 
45  818 
45  969 
46120 


39  846 
40019 
40192 

40  364 
40  535 

40  705 
40S75 
41044 
41212 
41380 

41547 
41714 
41880 
42  045 
42  210 

42  374 
42  537 
42  700 

42  862 

43  024 

43185 
43  345 
43  505 
43  664 
43  823 

43  981 

44  138 
44  295 
44  451 
44  607 

44  762 

44  917 

45  071 
45  225 
45  378 

45  530 
45  682 
45  834 
45  984 
46135 


46  270  46  285 
46  419  46434 
46  568  46  583 
46  716  46  731 
46  864  46879 


47  012 
47159 
47  305 
47  451 
47  5% 


47  026 
47173 
47  319 
47  465 
47  611 


39863 
40037 
40209  . 
40381 
40  552 

40  722 
40  892 
41061 
41229 
41397 

41564 
41731 
41896 
42  062 
42  226 

42  390 
42  553 
42  716 

42  878 

43  040 

43  201 
43  361 
43  521 
43  680 
43  838 

43  996 

44  154 
44  311 
44  467 
44623 

44  778 

44  932 

45  086 
45  240 
45  393 

45  545 
45  697 

45  849 
46000 
46150 

46  300 
46449 
46  598 

46  746 
46894 

47  041 
47188 
47  334 
47  480 
47  625 


6 


8 


9 


47  712  47  727  47  741  47  756  47  770 


39  881 
40054 
40226 

40  398 
40  569 


39  898 

40  071 
40  243 
40  415 
40  586 


40  739  40  756 
40  909  40926 
41078  41095 
41246  41263 
41414  41430 


N 


O 


41581 
41747 
41913 
42  078 
42  243 

42  406 
42  570 
42  732 

42  894 

43  056 

43  217 
43  377 
43  537 
43  696 

43  854 

44  012 
44170 
44  326 
44  483 
44  638 

44  793 

44  948 

45  102 

45  255 
45  408 

45  561 
45  712 

45  864 
46015 
46165 

46315 
46464 
46613 

46  761 
46909 

47  056 
47  202 
47  349 
47  494 
47  640 


41597 
41764 
41929 
42  095 
42  259 

42  423 
42  586 
42  749 

42  911 

43  072 

43  233 
43  393 
43  553 
43  712 

43  870 

44  028 
44  185 
44  342 
44  498 
44  654 

44  809 

44  963 
45117 

45  271 
45  423 

45  576 
45  728 

45  879 
46030 
46180 

46330 
46479 
46627 

46  776 
46923 

47  070 
47  217 
47  363 
47  509 
47  654 


39915 
40088 
40261 
40432 
40603 

40  773 
40  943 
41111 
41280 
41447 

41614 
41780 
41946 
42111 
42  275 

42  439 
42  602 
42  765 

42  927 

43  088 

43  249 
43  409 
43  569 
43  727 

43  886 

44  044 
44  201 
44  358 
44  514 


39933  39  950 
40106  40123 
40  278  40  295 
40449  40466 
40620  40637 

40  790  40807 
40960  40976 

41  128  41  145 
41296  41313 
41464  41481 


41  631 
41797 
41963 

42  127 
42  292 


41647 
41814 
41979 
42144 
42  308 


42  455  42  472 
42  619  42  635 
42  781  42  797 
42  943  42  959 
43104  43120 


43  265 
43  425 
43  584 
43  743 

43  902 

44  059 
44  217 
44  373 
44  529 


44669  44  685 


44  824 

44  979 

45  133 
45  286 
45  439 

45  591 
45  743 

45  894 
46045 
46195 

46345 
46494 
46642 

46  790 
46938 

47085 

47  232 
47  378 
47'524 
47  669 


44  840 

44  994 

45  148 
45  301 
45  454 

45  606 
45  758 

45  909 
46060 

46  210 

46359 
46-509 
46657 
46805 
46953 

47100 

47  246 
47  392 
47  538 
47  683 


43  281 
43  441 
43  600 
43  759 

43  917 

44  O/'; 
44  232 
44  389 
44  545 
44  700 

44  855 

45  010 
45  163 
45  317 
45  469 

45  621 
45  773 

45  924 
46075 

46  225 

46  374 
46  523 
46672 

46  820 
46967 

47  114 
47  261 
47  407 
47  553 
47  698 


47  784  47  799  47  813  47  828  47842 


8 


M 


:lJ 


250-300 


6 


300-360 


if 


307 
308 
309 

310 

311 
312 
313 
314 

315 

316 
317 
318 
319 

320 

321 
322 
323 
324 

325 

326 
327 
328 
329 

330 

331 
332 
333 
334 

335 

336 
337 
338 
339 

340 

341 
342 
343 
344 

345 

346 
347 
348 
349 

350 


K 


N 

O 

1 

2 

3 

4 

300 

47  712 

47  727 

47  741 

47  756 

47  770 

301 

47  857 

47  871 

47  885 

47  900 

47  914 

302 

48001 

48  015 

48  029 

480+4 

48  058 

303 

48144 

48159 

48173 

48187 

48  202 

304 

48  287 

48  302 

48  316 

48  330 

48  344 

305 

48430 

48  444 

48458 

48473 

48  487 

306 

48  572 

48  586 

48  601 

48  615 

48  629 

48  714  48  728  •18  742  48  7^.48  770 
48  855  48  869  48  883  48  897  48  911 

48  9%  49  010  49024  49  038  49052 

49136  49150  49164  49178  49192 

49276  49  290  49  304  49318  49  332 

49  415  49  429  49  443  49  457  49  471 
49  554  49  568  49  582  49  596  49  610 
49693  49  707  49  721  49  734  49  748 

49  831  49  845  49  859  49872  49886 

49  %9  49982  499%  50  010  50024 
50106  50120  50133  50147  50161 

50  243  50256  50  270  50  284  50  297 
50379  50  393  50406  50420  50433 

50515  50  529  50542  50  556  50  569 

50651  50664  50  678  50691  50  705 

50  786  50  799  50  813  50  826  50  840 
50920  50934  50^7  50  %1  50974 
51055  51068  51081  51095  51108 

51188  51202  51215  51228  51242 

51322  51335  51348  51362  51375 

51455  51468  51481  51495  51508 

51587  51601  51614  51627  51640 

51720  51733  51746  51759  51772 

51  851  51  865  51  878  51  891  51 90+ 
51 983  519%  52  009  52  022  52  035 
52114  52  127  52140  52153  52166 

52  244  52  257  52  270  52  284  52  297 
52  375  52  388  52  401  52  414  52  427 

52  504.52  517  52  530  52  543  52  556 

52  634  52  647  52  660  52  673  52  686 

52  763  52  776  52  789  52  802  52  815 

52  892  52  905  52  917  52  930  52  943 

53  020  53  033  53  0+6  53  058  53  071 

53148  53161  53173  53186  53199 

5>275  53  288  53  301  53  314  53  326 

53  403  53  415  53  428  53  441  53  453 

53  529  53  542  53  555  53  567  53  580 

53  656  53  668  53  681  53  694  53  706 

53  782  53  794  53  807  53  820  53  832 

53  908  53  920  53  933  53  945  53  958 

54  033  54  045  54  058  54070  54  083 
54158  54170  54183  54195  54  208 
54  283  54  29i  54  307  54  320  54  332 

54  407  54  419  54432  54444  54  456 


O 


6 


8 


9 


47  784  47  799  47  813  47  828  47842 

47  929-47  943  47  958  47  972  47  986 
48073  48  087  48101  48116  48130 

48  216  48  230  48  244  48  259  48  273 
48359  48  373  48387  48  401  48416 

48  501  48  515  48  530  48  544  48  558 

48643  48  657  48  671  48  686  48  700 

48  785  48  799  48  813  48  827  48  841 

48  926  48940  48954  48  968  48  982 
49066  49  080  49094  49108  49122 

49  206  49  220  49  234  49248  49  262 
49346  49  360  49  374  49  388  49  402 
49  485  49  499  49  513  49  527  49  541 
49624  49638  49651  49665  49  679 

49  762  49  776  49  790  49  803  49  817 

49900  49914  49927  49  941  49955 
50037  50051  50065  50079  50092 
50174  50188  50202  50  215  50229 
50311  50325  50338  50  352  50  365 
50447  50  461  50  474  50488  50  501 

50583  50  5%  50610  50623  50637 

50  718  50  732  50  745  50  759  50  772 
50  853  50  866  50  880  50  893  50907 
50987  51001  51014  51028  51041 
51121  51135  51148  51162  51175 

"51255  51268  51282  51295  51308 

51388  51402  51415  51428  51441 

51521  51534  51548  51561  51574 

51654  51667  51680  51693  51706 

51786  51799  51812  51825  51838 

51917  51930  51943  51957  51970 

52  048  52  061  52  075  52  088  52101 

52179  52192  52  205  52  218  52  231 

52  310  52  323  52  336  52  349  52  362 

52  440  52  453  52466  52  479  52  492 

52  569  52  582  52  595  52  608  52  621 

52  699  52  711  52  724  52  737  52  750 

52  827  52  840  52  853  52  866  52  879 

52  956  52  %9  52  982  52994  53  007 

53  084  53  097  53110  53122  53135 

53  212  53  224  53  237  53  250  53  263 

53  339  53  352  53  364  53  377  53  390 

53  466  53  479  53  491  53  504  53  517 

53  593  53  605  53  618  53  631  53  643 

53  719  53  732  53  744  53  757  53  769 

53  845  53  857  53  870  53  882  53  895 

53  970  53  983  53  995  54008  54  020 

54  095  54108  54120  54133  54145 
54  220  54  233  54  245  54  258  54  270 
54  345  54  357  54  370  54382  54  394 

54  469  54481  54  494  54  506  54  518 


5 


8 


300-360 


360-400 


N 


350 

351 
352 
353 
354 

355 

356 
357 
358 
359 

360 

361 
362 
363 
364 

365 

366 
367 
368 
369 

370 

371 
372 
373 
374 

375 

376 
377 
378 
379 

380 

381 
382 
383 
384 

385 

386 
387 
388 
389 

390 

391 
392 
393 
394 

395 

396 
397 
398 
399 

400 


O 


N 


54  407  54  419  54  432  54  444  54  456 

54  531  54  543  54  555  54  568  54  580 

54654  54  667  54  679  54  691  54  704 

54  777  54  790  54  802  54  814  54  827 
54900  54913  54  925  54937  54949 

55  023  55  035  55  047  55  060  55  072 
55  145  55  157  55169  55182  55194 
55  267  55  279  55  291  55  303  55  315 
55  388  55  400  55  413  55  425  55  437 
55  509  55  522  55  534  55  546  55  558 

55  630  55  642  55  654  55  666  55  678 

55  751  55  763  55  775  55  787  55  799 

55  871  55  883  55  895  55  907  55  919 

55  991  56003  56015  56  027  56038 
56110  56122  56134  56146  56158 

56229  56  241  56253  56  265  56  277 

56348  56360  56372  56384  56396 

56467  56478  56490  56  502  56  514 

56  585  56  597  56608  56620  56  632 

56  703  56  714  56  726  56  738  56  750 

56820  56832  56  844  56855  56867 

56937  56949  56  961  56  972  56984 

57  054  57  066  57  078  57  089  57101 
57171  57183  57194  57  206  57  217 
57  287  57  299  57  310  57  322  57  334 

57403  57415  57  426  57  438  57449 
57  519  57  530  57  542  57  553  57  565 
57634  57  646  57  657  57  669  57  680 
57  749  57  761  57  772  57  784  57  795 
57  864  57  875  57  887  57  898  5.7910 

57  978  57  990  58001  58013  58024 
58092  58104  58115  58127  58138 

58  206  58  218  58  229  58  240  58  252 
58320  58  331  58343  58354  58  365 
58433  58444  58456  58467  58478 

58  546  58  557  58  569  58  580  58  591 

58  659  58  670  58681  58  692  58  704 

58  771  58  782  58  794  58  805  58  816 
58883  58  894  58906  58917  58928 
58995  59006  59017  59028  590+0 

59106  59118  59129  59140  59151 

59  218  59  229  59  240  59  251  59  262 
59329  59340  59  351  59  362  59  373 
59439  59  450  59  461  59  472  59483 
59  550  59  561  59  572  59  583  59  594 

59660  59671  59682  59693  59  704 

59  770  59  780  59  791  59  802  59  813 

59879  59  890  59901  59  912  59923 

59988  59999  60  010  60021  60032 

60097  60108  60119  60130  60141 

60206  60217  60228  60239  60249 


6 


8 


9 


O 


54469  54481  54  494  54  506  54  518 

54  593  54  605  54617  54  630  54  642 

54  716  54  728  54  741  54  753  54  765 

54  839  54  851  54  86+  54  876  54  888 
54962  54974  54986  54998  55  011 

55  084  55  096  55108  55  121  55133 
55  206  55  218  55  230  55  242  55  255 
55  328  55  340  55  352  55  364  55  376 
55  449  55  461  55  473  55  485  55  497 
55  570  55  582  55  594  55  606  55  618 

55  691  55  703  55  715  55  727  55  739 

55  811  55  823  55  835  55  847  55  859 

55  931  55  943  55  955  55  %7  55  979 

56  050  56062  56074  56086  56098 
56170  56182  56194  56205  56  217 

56289  56301  56312  56324  56336 

56407  56419  56431  56443  56455 

56  526  56  538  56  549  56  561  56  573 

56  644  56656  56667  56  679  56  691 

56  761  56  773  56  785  56  797  56  808 

56879  56891  56902  56914  56926 

56996  57  008  57  019  57031  570+3 

57113  57124  57136  57148  57159 

57  229  57  241  57  252  57  264  57  276 
57  345  57357  57  368  57  380  57392 

57461  57473  57  484  574%  57  507 

57  576  57  588  57  600  57  611  57  623 

57  692  57  703  57  715  57  726  57  738 

57  807  57  818  57  830  57841  57  852 

57  921  57  933  57  944  57  955  57  %7 

58035  58047  58058  58070  58081 

58149  58161  58172  58184  58195 

58  263  58  274  58  286  58  297  58  309 
58  377  58  388  58  399  58410  58422 
58490  58  501  58  512  58  524  58  535 

58602  58614  58625  58636  58647 

58  715  58  726  58  737  58  749  58  760 

58  827  58  838  58  850  58  861  58872 
58939  58950  58961  58973  58984 
59051  59062  59073  59084  59095 

59162  59173  59184  59195  59  207 

59  273  59  284  59  295  59  306  59  318 
59  384  59395  59406  59  417  59428 
59494  59  506  59  517  59  528  59  539 
59605  59616  59627  59638  59  649 

59  715  59  726  59  737  59  748  59  759 

59  824  59  835  59  846  59  857  59  868 

59934  59  945  59956  59  966  59977 

60043  60054  60065  60076  60086 

60152  60163  60173  60184  60195 

60260  60271  60282  60293  60304 


6 


8 


9 


11 


360-400 


f 


8 


400-460 


t 


N 

O    1    2    3    4 

5    6    7    8    9 

400 

60  206  60  217  60  228  60  239  60  249 

60260  60271  60282  60293  60304 

401 

'60314  60  325  60  336  60347  60  358 

60369  60379  60390  60401  60412 

402 

60423  60433  60444  60455  60466 

60477  60  487  60498  60  509  60  520 

403 

60  531  60  541  60  552  60  563  60  574 

60  5S4  60  595  60  606  60  617  60  627 

4(H 

60638  606+9  60660  60670  60681 

60692  60  703  60  713  60  724  60  735 

405 

60  746  60  756  60  767  60  778  60  788 

60  799  60810  60821  60  831  60842 

406 

60853  60  863  60  874  60  885  60  895 

60906  60917  60927  60  938  60  9+9 

407 

60959  60  970  60981  60991  61002 

61013  61023  61034  61045  61055 

408 

61066  61077  61087  61098  61109 

61 119  61 130  61 140  61 151  61 162 

409 

61 172  61 183  61 194  61  2(H  61  215 

61225  61236  61247  61257  61268 

410 

61278  61289  61300  61310  61321 

61331  61342  61352  61363  61374 

411 

61384  61395  61405  61416  61426 

61437  61448  61458  61469  61479 

412 

61490  61500  61511  61521  61532 

61  542  61  553  61  563  61  574  61  584 

413 

61595  61606  61616  61627  61637 

616+8  61658  61669  61679  61690 

414 

61  700  61  711  61  721  61  731  61  742 

61752  61763  61773  61784  61794 

415 

61805  61815  61826  61836  61847 

61857  61868  61878  61888  61899 

416 

61909  61920  61930  61941  61951 

61962  61972  61982  61993  62  003 

417 

62  014  62  024  62  034  62  (H5  62  055 

62066  62  076  62  086  62  097  62107 

418 

62118  62128  62138  62149  62159 

62170  62  180  62  190  62  201  62  211 

419 

62  221  62  232  62  242  62  252  62  263 

62  273  62  284  62  294  62  304  62  315 

420 

62  325  62  335  62  346  62  356  62  366 

62  377  62  387  62  397  62  408  62  418 

421 

62  428  62  439  62  449  62  459  62  469 

62  480  62  490  62  500  62  511  62  521 

422 

62  531  62  542  62  552  62  562  62  572 

62  583  62  593  62  603  62  613  62  624 

423 

62  634  62  614  62  655  62  665  62  675 

62  685  62  696  62  706  62  716  62  726 

424 

62  737  62'747  62  757  62  767  62  778 

62  788  62  798  62  808  62  818  62  829 

425 

62  839  62  849  62  859  62  870  62  880 

62  890  62  900  62  910  62  921  62  931 

426 

62  9+1  62  951  62  %1  62  972  62  982 

62  992  63  002  63  012  63  022  63  033 

427 

63  (H3  63  053  63  063  63  073  63  083 

63  094  63  104  63114  63124  63134 

428 

63  144  63  155  63  165  63  175  63  185 

63195  63  205  63  215  63  225  63  236 

429 

63  246  63  256  63  266  63  276  63  286 

63  296  63  306  63  317  63  327  63  337 

430 

63  347  63  357  63  367  63  377  63  387 

63  397  63  407  63  417  63  428  63  438 

431 

63  448  63  458  63  468  63  478  63  488 

63  498  63  508  63  518  63  528  63  538 

432 

63  548  63  558  63  568  63  579  63  589 

63  599  63  609  63  619  63  629  63  639 

433 

63  6+9  63  659  63  669  63  679  63  689 

63  699  63  709  63  719  63  729  63  739 

434 

63  749  63  759  63  769  63  779  63  789 

63  799  63  809  63  819  63  829  63  839 

435 

63  849  63  859  63  869  63  879  63  889 

63  899  63  909  63  919  63  929  63  939 

436 

63  949  63  959  63  %9  63  979  63  988 

63  998  64  008  64  018  64  028  64038 

437 

6+0+8  6+058  64  068  64  078  64  088 

64  098  64108  6+118  64128  64137 

438 

64147  64157  64167  64177  64187 

64197  64  207  64  217  64  227  64  237 

439 

64  246  64  256  64  266  64  276  64  286 

64  296  64306  64  316  6+326  64  335 

440 

64  345  64355  64  365  64  375  64  385 

64  395  64404  64414  64+24  64434 

441 

64444  64454  64464  64473  64483 

64  493  64  503  64  513  64  523  64  532 

442 

64  542  64  552  6+562  64  572  64  582 

64  591  64  601  64  611  64  621  64  631 

443 

64  640  6+650  64  660  64  670  64  680 

64  689  6+699  64  709  64  719  64  729 

444 

6+738  6+748  64  758  64  768  64  777 

64  787  64  797  64  807  64  816  64  826 

445 

64  836  64  846  64  856  64  865  64  875 

64  885  64  895  64  904  64914  64924 

446 

64933  64943  64953  64%3  64972 

64  982  64  992  65  002  65  011  65  021 

447 

65  031  65  (HO  65  050  65  060  65  070 

65  079  65  089  65  099  65  108  65  118 

448 

65  128  65  137  65  147  65  157  65  167 

65  176  65  186  65  1%  65  205  65  215 

449 

65  225  65  234  65  244  65  254  65  263 

65  273  65  283  65  292  65  302  65  312 

450 

65  321  65  331  65  341  65  350  65  360 

65  369  65  379  65  389  65  398  65  408 

N 

O    1    2    3    4 

5    6    7    8    9 

400-460 


i 


450-600 

9 

N 

O 

1 

2 

3 

4 

5    6 

7 

8 

9 

450 

65  321 

65  331 

65  341 

65  350 

65  360 

65  369  65  379 

65  389 

65  398 

65  408 

451 

65  418 

65  427 

65  437 

65  447 

65  456 

65  466  65  475 

65  485 

65  495 

65  504 

452 

65  514 

65  523 

65  533 

65  543 

65  552 

65  562  65  571 

65  581 

65  591 

65  600 

453 

65  610 

65  619 

65  629 

65  639 

65  648 

65  658  65  667 

65  677 

65  686 

65  696 

454 

65  706 

65  715 

65  725 

65  734 

65  744 

65  753  65  763 

65  772 

65  782 

65  792 

455 

65  801 

65  811 

65  820 

65  830 

65  839 

65  849  65  858 

65  868 

65  877 

65  887 

456 

65  896  65  906 

65  916 

65  925 

65  935 

65  944  65  954 

65  963 

65  973 

65  982 

457 

65  992 

66001 

66011 

66020 

66030 

66039  66  0+9 

66  058 

66068 

66077 

458 

66087 

66096 

66106 

66115 

66124 

66134  66143 

66153 

66162 

66172 

459 

66181 

66191 

66  200 

66210 

66219 

66229  66  238 

66247 

66257 

66266 

460 

66  276 

66285 

66  295 

66304 

66314 

66323  66332 

66342 

66351 

66361 

461 

66  370 

66380 

66  389 

66  398 

66408 

66  417  66427 

66436 

66445 

66455 

462 

66  464 

66474 

66  483 

66492 

66  502 

66  511  66  521 

66530 

66  539 

66549 

463 

66  558 

66  567 

66  577 

66  586 

66  596 

66  605  66614 

66624 

66633 

66642 

464 

66652 

66661 

66671 

66680 

66689 

66699  66  708 

66  717 

66  727 

66  736 

465 

66  745 

66  755 

66  764 

66  773 

66  783 

66  792  66  801 

66  811 

66820 

66829 

466 

66839 

66  848 

66857 

66  867 

66876 

66885  66894 

66904 

66913 

66922 

467 

66932 

66941 

66950 

66960 

66969 

66978  66987 

66997 

67006 

67015 

468 

67  025 

67  034 

67  043 

67  052 

67  062 

67  071  67080 

67089 

67  099 

67108 

469 

67117 

67127 

67136 

67145 

67154 

67164  67173 

67182 

67191 

67  201 

470 

67210 

67219 

67  228 

67237 

67  247 

67  256  67  265 

67  274 

67  284 

67293 

471 

67  302 

67  311 

67  321 

67  330 

67  339 

67  3+8  67  357 

67  367  67  376  67  385  | 

472 

67  394 

67  403 

67413 

67  422 

67  431 

67440  67449 

67  459 

67468 

67  477 

473 

67486 

67  495 

67  504 

67  514 

67  523 

67  532  67  541 

67  550 

67  560 

67  569 

474 

67  578 

67  587 

67  596  67605 

67614 

67  624  67633 

67642 

67651 

67660 

475 

67669 

67679 

67688 

67697 

67  706 

67  715  67  724 

67  733 

67  742 

67  752 

476 

67  761 

67  770 

67  779 

67  788 

67  797 

67  806  67  815 

67  825 

67834 

67  843 

477 

67  852 

67  861 

67  870 

67  879 

67  888 

67  897  67906 

67  916 

67  925 

67934 

478 

679+3 

67952 

67961 

67970 

67  979 

67988  67997 

68006 

68015 

68024 

479 

68034 

68043 

68052 

68061 

68070 

68079  68088 

68097 

68106 

68115 

480 

68124 

68133 

68142 

68151 

68160 

68169  68178 

68187 

68196 

68  205 

481 

68215 

68  224 

68  233 

68  242 

68  251 

68  260  68  269 

68  278 

68  287 

68  2% 

482 

68305 

68  314 

68  323 

68332 

683+1 

68  350  68  359 

68  368 

68  377 

68  386 

483 

68395 

68  404 

68413 

68422 

68431 

68  440  68449 

68  458 

68467 

68  476 

484 

68485 

68494 

68  502 

68511 

68520 

68529  68  538 

68  547 

68556 

68565 

485 

68  574 

68  583 

68  592 

68601 

68  610 

68619  68628 

68637 

68646 

68655 

486 

68  664 

68673 

68  681 

68  690 

68699 

68  708  68  717 

68  726 

68  735 

68  744 

487 

68  753 

68  762 

68  771 

68  780 

68  789 

68  797  68  806 

68  815 

68  824 

68  833 

488 

68842 

68  851 

68  860 

68  869 

68  878 

68  886  68895 

68904 

68913 

68922 

489 

68931 

68940 

68949 

68958 

68966 

68975  68984 

68993 

69002 

69011 

490 

69020 

69028 

69037 

69046 

69055 

69064  69073 

69082 

69090  69099  | 

491 

69108 

69117 

69126 

69135 

69144 

69152  69161 

69170 

69179 

69188 

492 

69197 

69  205 

69  214 

69  223 

69  232 

69  241  69  249 

69  258 

69  267 

69  276 

493 

69  285 

69  294 

69  302 

69  311 

69  320 

69329  69338 

69346 

69  355 

69  364 

494 

69373 

69381 

69390 

69399 

69408 

69417  69425 

69434 

69443 

69452 

495 

69  461 

69  469 

69  478 

69487 

69496 

69  504  69  513 

69  522 

69  531 

69  539 

496 

69  5+8 

69  557 

69  566 

69  574 

69  583 

69  592  69601 

69609  69618  69627  | 

497 

69  636 

69  644 

69  653 

69  662 

69  671 

69679  69  688 

69697 

69  705 

69  714 

498 

69  723 

69  732 

69  740 

69  749 

69  758 

69  767  69  775 

69  784 

69  793 

69  801 

499 

69  810 

69  819 

69827 

69  836 

69  845 

69  854  69862 

69871 

69880 

69888 

500 

69  897 

69906 

69914 

69923 

69932 

69940  69949  69958  69966  69975  1 

N 

0 

1 

2 

3 

4 

5    6 

7 

8 

• 

I  k 


n\ 


460-600 


10 


500  -  550 


650-600 


11 


« 


I 


I 


N 

O    1    2    3    4 

5    6    7    8    9 

1 

500 

69  897  69906  69  914  69923  69932 

69940  69  949  69958  69  966  69975 

501 

69  984  69992  70  001  70  010  70  018 

70027  7/)  036  70  (H4  70  053  70062 

502 

70070  70  079  70088  70096  70  lOi 

70114  70122  70131  70140  70148 

503 

70157  70165  70174  70 183  70191 

70  200  70  209  70  217  70  226  70  234 

5(H 

70  243  70  252  70  260  70  2^9  70  278 

70  286  70  295  70303  70312  70321 

505 

70329  70338  70  346  7035i  70364 

70372  70381  70389  70398  70406 

506 

70  415  70424  70432  70441  70449 

70458  70467  70  475  70484  70492 

507 

70  501  70  509  70  518  70  526  70  535 

70  544  70  552  70  561  70  569  70  578 

508 

70  586  70  59i  70603  70  612  70621 

70629  70  638  70  646  70  655  70  663 

509 

70672  70680  70689  70697  70  706 

70  714  70  723  70  731  70  740  70  749 

510 

70  757  70  766  70  774  70  783  70  791 

70800  70808  70  817  70825  70  834 

511 

70842  70851  70  859  70868  70  876 

70885  70  893  70  902  70910  70919 

512 

70927  70935  70944  70952  70  %1 

70  %9  70978  70  986  70  995  71003 

513 

71012  71020  71029  71037  71046 

71054  71063  71071  71079  71088 

514 

71096  71105  71113  71122  71130 

71139  71147  71155  71164  71172 

515 

71181  71189  71198  71206  71214 

71223  71231  71240  71248  71257 

516 

7126i  71273  71282  71290  71299 

71307  71315  71324  71332  71341 

517 

71349  71357  71366  71374  71383 

71391  71399  71408  71416  71425 

518 

71433  71441  71450  71458  71466 

71475  71483  71492  71500  71508 

519 

71517  71525  71533  71542  71550 

71559  71567  71575  71584  71592 

520 

71600  71609  71617  71625  71634 

71642  71650  71659  71667  71675 

521 

71684  71692  71700  71709  71717 

71725  71734  71743  71750  71759 

522 

71767  71775  71784  71792  71800 

71809  71817  71825  71834  71842 

523 

71850  71858  71867  71875  71883 

71892  71900  71908  71917  71925 

524 

71933  71941  71950  71958  71966 

71975  71983  71991  71999  72  008 

525 

72  016  72  024  72  032  72  041  72  049 

72  057  72  066  72  074  72  082  72  090 

526 

72  099  72107  72115  72123  72132 

72140  72  148  72156  72165  72173 

527 

72181  72  189  72198  72  206  72  214 

72  222  72  230  72  239  72  247  72  255 

528 

72  263  72  272  72  280  72  288  72  2% 

72  304  72  313  72  321  72  329  72  337 

529 

72  346  72  354  72  362  72  370  72  378 

72  387  72  395  72  403  72  411  72  419 

530 

72  428  72  436  72  444  72  452  72  460 

72  469  72  477  72  485  72  493  72  501 

531 

72  509  72  518  72  526  72  534  72  542 

72  550  72  558  72  567  72  575  72  583 

532 

72  591  72  599  72  607  72  616  72  624 

72  632  72  640  72  648  72  656  72  665 

533 

72  673  72  681  72  689  72  697  72  705 

72  713  72  722  72  730  72  738  72  746 

534 

72  754  72  762  72  770  72  779  72  787 

72  795  72  803  72  811  72  819  72  827 

535 

72  835  72  843  72  852  72  860  72  868 

72  876  72  884  72  892  72  900  72  908 

536 

72  916  72  925  72  933  72  941  72  949 

72  957  72  %5  72  973  72  981  72  989 

537 

72  997  73  006  73  014  73  022  73  030 

73  038  73  046  73  054  73  062  73  070 

538 

73  078  73  086  73  094  73  102  73  111 

73119  73127  73135  73  143  73151 

539 

73159  73167  73175  73  183  73  191 

73199  73  207  73  215  73  223  73  231 

540 

73  239  73  247  73  255  73  263  73  272 

73  280  73  288  73  2%  73  304  73  312 

541 

73  320  73  328  73  336  73  344  73  352 

73  360  73  368  73  376  73  384  73  392 

542 

73  400  73  408  73  416  73  424  73  432 

73  440  73  448  73  456  73  464  73  472 

543 

73  480  73  488  73  496  73  504  73  512 

73  520  73  528  73  536  73  544  73  552 

544 

73  560  73  568  73  576  73  584  73  592 

73  600  73  608  73  616  73  624  73  632 

545 

73  640  73  648  73  656  73  664  73  672 

73  679  73  687  73  695  73  703  73  711 

546 

73  719  73  727  73  735  73  743  73  751 

73  759  73  767  73  775  73  783  73  791 

547 

73  799  73  807  73  815  73  823  73  830 

73  838  73  846  73  854  73  862  73  870 

548 

73  878  73  886  73  894  73  902  73  910 

73  918  73  926  73  933  73  941  73  949 

549 

73  957  73  %5  73  973  73  981  73  989 

73  997  74  005  74  013  74  020  74028 

550 

74  036  74  OH  74  052  74  060  74  068 

74076  74084  74092  74099  74107 

N 

0    12    3    4 

5    6    7    8    9   1 

N 


550 

551 
552 
553 
554 

555 

556 
557 
558 
559 

560 

561 
562 
563 
564 

565 

566 
567 
568 
569 

570 

571 
572 
573 
574 

575 

576 

577 
578 
579 

580 

581 
582 
583 
584 

585 

586 
587 
588 
589 

590 

591 
592 
593 
594 

595 

5% 
597 
598 
599 

600 


N 


o 

1 

2 

3 

4 

5 

6 

7 

8 

9 

74  036 

74  (H4 

74  052 

74  060 

74  068 

74  076 

74  084 

74  092 

74  099 

74107 

74115 

74123 

74131 

74139 

74147 

74155 

74162 

74170 

74178 

74186 

74194 

74  202 

74  210 

74  218 

74  225 

74  233 

74  241 

74  249 

74  257 

74  265 

74  273 

74  280 

74  288 

74  2% 

74  304 

74  312 

74  320 

74  327 

74  335 

74  343 

74351 

74359 

74367 

74  374 

74  382 

74  390 

74  398 

74  406 

74414 

74421 

74429 

74437 

74  445 

74  453 

74  461 

74  468 

74  476 

74484 

74  492 

74  500 

74  507 

74  515 

74  523 

74  531 

74  539 

74  547 

74  554 

74  562 

74  570 

74  578 

74  586 

74  593 

74  601 

74  609 

74  617 

74  624 

74  632 

74  640 

74  648 

74  656 

74  663 

74  671 

74  679 

74  687 

74  695 

74  702 

74  710 

74  718 

74  726 

74  733 

74  741 

74  749 

74  757 

74  764 

74  772 

74  780 

74  788 

74  7% 

74  803 

74  811 

74  819 

74  827 

74  834 

74  842 

74  850 

74  858 

74  865 

74  873 

74  881 

74  889 

74  8% 

74  904 

74  912 

74  920 

74  927 

74  935 

74  943 

74  950 

74958 

74966 

74  974 

74981 

74989 

74  997 

75  005 

75  012 

75  020 

75  028 

75  035 

75  043 

75  051 

75  059 

75  066 

75  074 

75  082 

75  089 

75  097 

75105 

75113 

75120 

75128 

75136 

75143 

75151 

75159 

75  166 

75174 

75182 

75189 

75197 

75  205 

75  213 

75  220 

75  228 

75  236 

75  243 

75  251 

75  259 

75  266 

75  274 

75  282 

75  289 

75  297 

75  305 

75  312 

75  320 

75  328 

75  335 

75  343 

75  351 

75  358 

75  366 

75  374 

75  381 

75  389 

75  397 

75  404 

75  412 

75  420 

75  427 

75  435 

75  442 

75  450 

75  458 

75  465 

75  473 

75  481 

75  488 

75  4% 

75  504 

75  511 

75  519 

75  526 

75  534 

75  542 

75  549 

75  557 

* 

75  565 

75  572 

75  580 

75  587 

75  595 

75  603 

75  610 

75  618 

75  626 

75  633 

75  641 

75  648 

75  656 

75  664 

75  671 

75  679 

75  686 

75  694 

75  702 

75  709 

75  717 

75  724 

75  732 

75  740 

75  747 

75  75i 

75  762 

75  770 

75  778 

75  785 

75  793 

75  800 

75  808 

75  815 

75  823 

75  831 

75  838 

75  846 

75  853 

75  861 

75  868 

75  876 

75  884 

75  891 

75  899 

75  906 

75  914 

75  921 

75  929 

75  937 

75  944 

75  952 

75  959 

75  967 

75  974 

75  982 

75  989 

75  997 

76005 

76012 

76020 

76027 

76035 

76042 

76050 

76057 

76065 

76072 

76080 

76087 

76095 

76103 

76110 

76118 

76125 

76133 

76140 

76 148 

76 155- 

76163 

76170 

76178 

76185 

76193 

76  200 

76  208 

76  215 

76223 

76  230 

76  238 

76  245 

76  253 

76  260 

76268 

76275 

76283 

76290 

76298 

76305 

76313 

76320 

76328 

76335 

76343 

76350 

76358 

76365 

76373 

76380 

76388 

76395 

76403 

76410 

76418 

76425 

76  433 

76440 

76  448 

76455 

76462 

76470 

76477 

76485 

76492 

76  500 

76  507 

76  515 

76  522 

76  530 

76  537 

76  545 

76  552 

76  559 

76  567 

76  574 

76  582 

76  589 

76  597 

76604 

76612 

76619 

76626 

76634 

76641 

76649 

76656 

76664 

76671 

76678 

76686 

76693 

76  701 

76  708 

76  716 

76  723 

76  730 

76  738 

76  745 

76  753 

76  760 

76  768 

76  775 

76  782 

76  790 

76  797 

76  805 

76  812 

76  819 

76827 

76  834 

76842 

76849 

76856 

76864 

76871 

76  879 

76  886 

76893 

76901 

76908 

76916 

76923 

76  930 

76938 

76945 

76  953 

76960 

76967 

76975 

76982 

76989 

76997 

77004 

77012 

77019 

77  026 

77034 

77  041 

77  048 

77  056 

77  063 

77  070 

77  078 

77085 

77093 

77100 

77107 

77115 

77122 

77129 

77137 

77144 

77151 

77159 

77166 

77173 

77181 

77  188 

77195 

77  203 

77  210 

77  217 

77  225 

77  232 

77  240 

77  247 

77  254 

77  262 

77  269 

77  276 

77  283 

77  291 

77  298 

77305 

77  313 

77  320 

77  327 

77335 

77  342 

77  349 

77  357 

77  364 

77371 

77379 

77386 

77  393 

77  401 

77408 

77  415 

77  422 

77  430 

77  437 

77  444 

77452 

77459 

77466 

77474 

77481 

77488 

77495 

77  503 

77  510 

77  517 

77  525 

77  532 

77  539 

77  546 

77  554 

77  561 

77  568 

77  576 

77  583 

77  590 

77  597 

77  605 

77  612 

77619 

77  627 

77  634 

77  641 

77  648 

77  656 

77  663 

77670 

77  677 

77  685 

77  692 

77  699 

77  706 

77  714 

77  721 

77  728 

77  735 

77  743 

77  750 

77  757 

77  764 

77  772 

77  779 

77  786 

77  793 

77  801 

77  808 

77815 

77  822 

77830 

77837 

77844 

77851 

77859 

77  866 

77873 

77880 

O 

1 

2 

3 

4 

5 

6 

7 

8 

9 

500-550 


650-600 


12 


600-650 


660-700 


18 


I  ^^ 


t 


'1 


N 


600 

601 
602 
603 
604 

605 

606 
607 
608 
609 

610 

611 
612 
613 
614 

615 

616 
617 
618 
619 

620 

621 
622 
623 
624 

625 

626 
627 
628 
629 

630 

631 
632 
633 
634 

635 

636 
637 
638 
639 

640 

6+1 
612 
643 
6H 

645 

6+6 
647 
648 
649 

650 


O 


77  815  77  822  77  830  77  837  77  844 

77  887  77  895  77  902  77  909  77  916 

77  960  77  967  77  974  77981  77  988 
78032  78  039  78  (H6  78  053  78061 
78104  78111  78118  78125  78132 

78176  78183  78190  78197  78  204 

78  247  .78  254  78  262  78  269  78  276 
78  319  78  326  78  333  78  340  78  347 
78  390  78  398  78  405  78  412  78  419 
78  462  78  469  78476  78  483  78  490 

78  533  78  540  78  547  78  554  78  561 

78  6(H  78611  78  618  78  625  78  633 

78  675  78  682  78  689  78  696  78  704 

78  746  78  753  78  760  78  767  78  774 

78817  78  824  78  831  78  838  78  845 

78  888  78895  78902  78  909  78916 

78  958  78  %5  78972  78  979  78  986 
79029  79  036  79043  79050  79  057 
79099  79106  79113  79120  79127 
79169  79176  79183  79190  79197 

79  239  79  246  79  253  79  260  79  267 
79309  79  316  79  323  79  330  79  337 
79  379  79  386  79  393  79400  79407 
79449  79  456  79463  79470  79477 
79  518  79  525  79  532  79  539  79  546 

79  588  79  595  79602  79609  79  616 

79657  79  66+  79  671  79  678  79  685 

79  727  79  734  79  741  79  748  79  754 

79  7%  79  803  79  810  79  817  79  824 
79865  79  872  79  879  79  886  79  893 

79934  79^1  79^8  79955  79962 

80  003  80010  80017  80024  80030 
80  072  80079  80  085  80  092  80  099 
80140  80147  80154  80161  80168 
80  209  80  216  80  223  80  229  80  236 

80  277  80  284  80  291  80  298  80  305 

80  346  80  353  80  359  80  366  80  373 

80414  80  421  80428  80  434  80  441 

80  482  80  489  80  496  80  502  80  509 

80  550  80  557  80  564  80  570  80  577 

80618  80625  80632  80638  806+5 

80  686  80  693  80  699  80  706  80  713 

80  754  80  760  80  767  80  774  80  781 

80  821  80  828  80  835  80  841  80  848 

80889  80  895  80  902  80909  80  916 

80956  80  %3  80969  80976  80983 

81023  81030  81037  81043  81050 

81090  81097  81104  81111  81117 

81158  81164  81171  81178  81184 

81224  81231  81238  81 245  81 251 

81291  81298  81305  81311  81318 


6 


8 


9 


O 


77  851  77  859  77  866  77  873  77  880 

77  924  77  931  77  938  77  945  77  952 
779%  78  003  78010  78  017  78  025 

78  068  78  075  78082  78  089  78  097 
78140  78147  78154  78161  78168 

78  211  78  219  78  226  78  233  78  240 

78  283  78  290  78  297  78  305  78  312 

78355  78  362  78  369  78  376  78  383 

78  426  78433  78  440  78  447  78  455 

78497  78  504  78  512  78  519  78  526 

78  569  78  576  78  583  78  590  78  597 

78  6+0  78  647  78  654  78  661  78  668 

78  711  78  718  78  725  78  732  78  739 

78  781  78  789  78  7%  78  803  78  810 

78  852  78  859  78  866  78  873  78  880 

78  923  78930  78937  78  944  78951 

78  993  79000  79  007  79  014  79  021 
79064  79  071  79  078  79085  79  092 
79134  79141  79148  79155  79  162 

79  20+  79  211  79  218  79  225  79  232 

79  274  79  281  79  288  79  295  79302 

79  344  79  351  79  358  79  365  79  372 

79  414  79  421  79  428  79  435  79  442 

79  484  79  491  79  498  79  505  79  511 

79  553  79  560  79  567  79  574  79  581 

79623  79630  79  637  79  644  79  650 

79  692  79  699  79  706  79  713  79  720 

79  761  79  768  79  775  79  782  79  789 

79  831  79  837  79  844  79  851  79  858 

79900  79  906  79913  79  920  79927 

79  %9  79975  79982  79989  799% 

80  037  80  044  80051  80  058  80  065 
80106  80113  80120  80127  80134 
80175  80 182  80188  80195  80  202 
80  243  80  250  80  257  80  264  80  271 

80  312  80318  80  325  80  332  80  339 

80  380  80  387  80  393  80  400  80407 

80  448  80  455  80  462  80  468  80  475 

80  516  80  523  80  530  80  536  80  543 

80  584  80  591  80  598  80604  8061i 

80652  80659  80665  80672  80679 

80  720  80  726  80  733  80  740  80  747 

80  787  80  794  80  801  80  808  80  814 

80  855  80  862  80  868  80  875  80  882 
80922  80929  80  936  80943  80949 

80990  809%  81003  81010  81017 

81057  81064  81070  81077  81084 

81  124  81  131  81  137  81  144  81 151 
81  191  81  198  81  20+  81  211  81  218 
81258  81265  81271  81278  81 28i 

8132i  81331  81338  81345  81351 


6 


8 


9 


N 


650 

651 
652 
653 
654 

655 

656 
657 
658 
659 

660 

661 
662 
663 
664 

665 

666 
667 
668 
669 

670 

671 
672 
673 
674 

675 

676 
677 
678 
679 

680 

681 
682 
683 
684 

685 

686 
687 
688 
689 

690 

691 
692 
693 
694 

695 

696 
697 
698 
699 

TOO 


N 


O 


81291  81298  81305  81311  81318 

81358  81365  81371  81378  81385 

81425  81431  81438  81445  81451 

81491  81498  81505  81511  81518 

81558  81564  81571  81578  81584 

81624  81631  81637  81644  81651 

81 690  81  697  81  704  81  710  81  717 

81757  81763  81770  81776  81783 

81823  81829  81836  81842  81849 

81889  81895  81902  81908  81915 

81954  81961  81  %8  81974  81981 

82  020  82  027  82  033  82  040  82  046 

82  086  82  092  82  099  82105  82112 

82151  82158  82164  82171  82178 

82  217  82  223  82  230  82  236  82  243 

82  282  82  289  82  295  82  302  82  308 

82  347  82  354  82  360  82  367  82  373 

82  413  82  419  82  426  82  432  82  439 

82  478  82  484  82  491  82  497  82  504 

82  543  82  549  82  556  82  562  82  569 

82  607  82  614  82  620  82  627  82  633 

82  672  82  679  82  685  82  692  82  698 

82  737  82  743  82  750  82  756  82  763 

82  802  82  808  82  814  82  821  82  827 

82  866  82  872  82  879  82  885  82  892 

82  930  82  937  82  943  82950  82  956 

82  995  83  001  83  008  83  014  83  020 

83  059  83  065  83  072  83  078  83  085 
83123  83  129  83  136  83142  83149 
83  187  83  193  83  200  83  206  83  213 

83  251  83  257  83  264  83  270  83  276 

83  315  83  321  83  327  83  334  83  340 

83  378  83  385  83  391  83  398  83  404 

83  442  83  448  83  455  83  461  83  467 

83  506  83  512  83  518  83  525  83  531 

83  569  83  575  83  582  83  588  83  594 

83  632  83  639  83  645  83  651  83  658 

83  696  83  702  83  708  83  715  83  721 

83  759  83  765  83  771  83  778  83  784 

83  822  83  828  83  835  83  841  83  847 

83  885  83  891  83  897  83  904  83  910 

83  948  83  954  83  960  83  967  83  973 
84011  84  017  84  023  84  029  84  036 
84073  84  080  84  086  84092  84  098 
84136  84142  84148  84155  84161 

84198  84  205  84  211  84  217  84  223 

84  261  84  267  84  273  84  280  84  286 
84  323  84  330  84  336  84  342  84  348 
84  386  84  392  84  398  84  404  84  410 
84  448  84  454  84  460  84  466  84  473 

84  510  84  516  84  522  84  528  84  535 


O 


81325 
81391 
81458 
81525 
81591 

81657 
81723 
81790 
81856 
81921 

81987 
82  053 
82119 
82184 
82  249 

82  315 


6 

7 

8 

9 

5  81331 

81338 

81345 

81351 

I  81398 

81405 

81411 

81418 

3  81465 

81471 

81478 

81485 

5  81531 

81538 

81544 

81551 

I  81598 

81604 

81611 

81617 

7   81664 

81671 

81677 

81684 

5  81730 

81737 

81743 

81750 

)  81796 

81803 

81809 

81816 

S  81862 

81869 

81875 

81882 

L  81928 

81935 

81941 

81948 

1   81994 

82  000 

82  007 

82  014 

\   82060 

82  066 

82  073 

82  079 

}   82125 

82132 

82138 

82145 

1-  82191 

82197 

82  204 

82  210 

)  82  256 

82  263 

82  269 

82  276 

;  82  321 

82  328 

82  334 

82  341 

82  380  82  387  82  393  82  400  82  406 

82  445  82  452  82  458  82  465  82  471 

82  510  82  517  82  523  82  530  82  536 

82  575  82  582  82  588  82  595  82  601 

82  640  82646  82653  82  659  82  666 
82  705  82  711  82  718  82  724  82  730 
82  769  82  776  82  782  82  789  82  795 
82  834  82  840  82  847  82  853  82  860 
82  898  82  905  82  911  82  918  82  924 

82  963  82  969  82  975  82  982  82  988 

83  027  83  033  83  0+0  83  046  83  052 
83  091  83  097  83104  83110  83117 
83155  83161  83168  83  174  83  181 
83  219  83  225  83  232  83  238  83  245 

83  283  83  289  83  2%  83  302  83  308 

83  347  83  353  83  359  83  366  83  372 

83  410  83  417  83  423  83  429  83  436 

83  474  83  480  83  487  83  493  83  499 

83  537  83  544  83  550  83  556  "83  563 

83  601  83  607  83  613  83  620  83  626 

83  664  83  670  83  677  83  683  83  689 

83  727  83  734  83  740  83  746  83  753 

83  790  83  797  83  803  83  809  83  816 

83  853  83  860  83  866  83  872  83  879 

83  916  83  923  83  929  83  935  83  942 

83  979  83  985  83  992  83  998  84  004 
84042  84  048  84  055  84  061  84  067 
84105  84111  84117  84123  84130 
84167  84173  84180  84186  84192 

84  230  84  236  84  242  84  248  84  255 
84  292  84  298  84  305  84  311  84  317 
84  354  84  361  84  367  84  373  84379 
84417  84423  84429  84  435  84  442 
84  479  84485  84  491  84  497  84  504 

84  541  84  547  84  553  84  559  84  566 


6 


8 


9 


600-660 


660  -  700 


14 


700-760 


tji 


k       f 


^ 


'■ 


N 

O 

1 

2    3 

4 

5    6    7    8    9 

700 

84  510 

84  516 

84  522  84  528  84  535 

84  541  84  547  84  553  84  559  84  566 

701 

84  572 

84  578 

84  584  84  590 

84  597 

84  603  84  609  84  615  84  621  84  628 

702 

84634 

84  640 

84  646  84  652 

84  658 

84665  84671  84677  84683  84689 

703 

846% 

84  702 

84  708  84  714 

84  720 

84  726  84  733  84  739  84  745  84  751 

704 

84  757 

84  763 

84  770  84  776 

84  782 

84  788  84  794  84  800  84  807  84  813 

706 

84  819 

84  825 

84  831  84  837 

84  844 

84  850  84  856  84  862  84  868  84  874 

706 

84  880 

84  887 

84  893  84  899 

84  905 

84  911  84  917  84  924  84  930  84  936 

707 

84  942 

84  948 

84  954  84  960 

84  %7 

84  973  84  979  84  985  84  991  84  997 

708 

85  003 

85  009 

85  016  85  022 

85  028 

85  034  85  040  85  046  85  052  85  058 

709 

85  065 

85  071 

85  077  85  083 

85  089 

85  095  85  101  85  107  85  114  85  120 

710 

85  126 

85132 

85  138  85  144 

85150 

85156  85163  85169  85175  85181 

711 

85  187 

85  193 

85  199  85  205 

85  211 

85  217  85  224  85  230  85  236  85  242 

712 

85  248 

85  254 

85  260  85  266 

85  272 

85  278  85  285  85  291  85  297  85  303 

713 

85  309 

85  315 

85  321  85  327 

85  333 

85  339  85  345  85  352  85  358  85  364 

714 

85  370 

85  376 

85  382  85  388 

85  394 

85  400  85  406  85  412  85  418  85  425 

715 

85  431 

85  437 

85  443  85  449 

85  455 

85  461  85  467  85  473  85  479  85  485 

716 

85  491 

85  497 

85  503  85  509 

85  516 

85  522  85  528  85  534  85  540  85  546 

717 

85  552 

85  558 

85  564  85  570 

85  576 

85  582  85  588  85  594  85  600  85  606 

718 

85  612 

85  618 

85  625  85  631 

85  637 

85  643  85  649  85  655  85  661  85  667 

719 

85  673 

85  679  85  685  85  691 

85  697 

85  703  85  709  85  715  85  721  85  727 

720 

85  733 

85  739 

85  745  85  751 

85  757 

85  763  85  769  85  775  85  781  85  788 

721 

85  794 

85  800 

85  806  85  812 

85  818 

85  824  85  830  85  836  85  842  85  848 

722 

85  854 

85  860 

85  866  85  872 

85  878 

85  884  85  890  85  8%  85  902  85  908 

723 

85  914 

85  920 

85  926  85  932 

85  938 

85  944  85  950  85  956  85  %2  85  968 

724 

85  974 

85  980 

85  986  85  992 

85  998 

86004  86010  86016  86022  86028 

725 

86034 

86040 

86046  86052 

86058 

86064  86070  86076  86082  86088 

726 

86094 

86100 

86106  86112 

86118 

86124  86130  86136  86141  86147 

727 

86153 

86159 

86165  86171 

86177 

86183  86189  86195  86  201  86  207 

728 

86  213 

86  219 

86  225  86  231 

86  237 

86  243  86  249  86  255  86  261  86  267 

729 

86273 

86279  86  285  86291 

86  297 

86  303  86  308  86314  86  320  86326 

730 

86332 

86338 

86344  86350 

86  356 

86362  86368  86374  86380  86386 

731 

86392 

86  398 

86404  86410 

86  415 

86  421  86  427  86  433  86  439  86445 

732 

86451 

86457 

86463  86469  86475 

86481  86487  86493  86499  86504 

733 

86510 

86  516 

86  522  86  528 

86  534 

86  540  86  546  86  552  86  558  86564 

734 

86570 

86  576 

86  581  86  587 

86  593 

86599  86605  86611  86617  86623 

735 

86629  86635 

86641  86646 

86652 

86658  86664  86670  86676  86682 

736 

86688 

86  694 

86  700  86  705 

86  711 

86  717  86  723  86  729  86  735  86  741 

737 

86  747 

86  753 

86  759  86  764 

86  770 

86  776  86  782  86  788  86  794  86800 

738 

86806 

86  812 

86  817  86  823 

86  829 

86  835  86841  86  847  86853  86  859 

739 

86864 

86870 

86876  86  882 

86  888 

86894  86900  86906  86911  86917 

740 

86923 

86929 

86935  86  941 

86947 

86953  86958  86964  86970  86976 

741 

86982 

86988 

86994  86  999 

87  005 

87  011  87  017  87023  87029  87035 

742 

87040 

87  046 

87052  87  058 

87  064 

87  070  87  075  87081  87  087  87  093 

743 

87099 

87105 

87111  87116 

87122 

87128  87134  87140  87146  87151 

744 

87157 

87163 

87169  87175 

87181 

87186  87192  87198  87  204  87  210 

745 

87  216 

87  221 

87  227  87  233 

87  239 

87  245  87  251  87  256  87  262  87  268 

746 

87  274 

87  280 

87  286  87  291 

87  297 

87303  87  309  87  315  87  320  87326 

747 

87  332 

87  338 

87  344  87  349 

87  355 

87  361  87  367  87  373  87  379  87  384 

748 

87  390 

87  3% 

87  402  87  408 

87413 

87  419  87  425  87  431  87  437  87442 

749 

87  448 

87454 

87  460  87  466 

87  471 

87  477  87  483  87  489  87  495  87  500 

750 

87506 

87  512 

87  518  87  523 

87  529 

87  535  87  541  87  547  87  552  87  558 

N 

0 

1 

2    3 

4 

5    6    7    8    9 

700-760 


750-800 


15 


N 

0    12    3    4 

5    6 

7    8    9 

750 

87  506  87  512  87  518  87  523  87  529 

87  535  87  541 

87  547  87  552  87  558 

751 

87  564  87  570  87  576  87  581  87  587 

87  593  87  599 

87604  87  610  87  616 

752 

87  622  87  628  87  633  87639  87645 

87  651  87656 

87  662  87668  87  674 

753 

87  679  87685  87  691  87697  87  703 

87  708  87  714 

87  720  87  726  87  731 

754 

87  737  87  743  87  749  87  754  87  760 

87  766  87  772 

87  777  87  783  87  789 

755 

87  795  87  800  87  806  87  812  87818 

87  823  87  829 

87  835  87841  87  846 

756 

87  852  87  858  87  864  87  869  87  875 

87  881  87  887 

87  892  87  898  87904 

757 

87  910  87915  87  921  87927  87933 

87  938  87944 

87  950  87  955  87  %1 

758 

87  %7  87973  87978  87  984  87  990 

879%  88  001 

88007  88013  88018 

759 

88024  88030  88036  88041  88047 

88053  88058 

88064  88070  88076 

760 

88081  88087  88093  88098  88104 

88110  88116 

88121  88127  88133 

761 

88138  88144  88150  88156  88161 

88167  88173 

88178  88184  88190 

762 

88195  88  201  88  207  88  213  88  218 

88  224  88  230 

88  235  88  241  88247 

763 

88  252  88  258  88  264  88  270  88  275 

88  281  88  287 

88  292  88298  88304 

764 

88309  88  315  88321  88326  88332 

88338  88343 

88349  88  355  88360 

765 

88366  88  372  88  377  88  383  88  389 

88  395  88400 

88406  88412  88417 

766 

88423  88  429  88434  88  440  88446 

88451  88457 

88463  88468  88474 

767 

88480  88485  88491  88497  88  502 

88  508  88  513 

88  519  88525  88  530 

768 

88  536  88  542  88  547  88  553  88  559 

88  564  88  570 

88  576  88  581  88  587 

769 

88  593  88  598  88604  88  610  88615 

88621  88  627 

88632  88638  88643 

770 

88  649  88  655  88  660  88666  88672 

88677  88683 

88689  88694  88  700 

771 

88  705  88  711  88  717  88  722  88  728 

88  734  88  739  88  745  88  750  88  756  1 

772 

88  762  88  767  88  773  88  779  88  784 

88  790  88  795 

88  801  88807  88812 

773 

88818  88  824  88  829  88835  88  840 

88846  88  852 

88857  88863  88868 

774 

88874  88880  88  885  88  891  88  897 

88902  88908 

88913  88919  88925 

775 

88930  88936  88941  88947  88953 

88958  88964 

88  %9  88975  88981 

776 

88986  88992  88997  89003  89009 

89014  89020 

89025  89031  89037 

777 

89042  89048  89053  89059  89064 

89070  89076 

89081  89087  89092 

778 

89098  89104  89109  89115  89120 

89126  89131 

89137  89143  89148 

779 

89154  89159  89165  89170  89176 

89182  89187 

89193  89198  89204 

780 

89209  89  215  89221  89  226  89232 

89  237  89  243 

89  248  89  254  89260 

781 

89  265  89  271  89  276  89  282  89  287 

89  293  89  298 

89304  89  310  89315 

782 

89321  89  326  89  332  89337  89343 

89348  89  354 

89360  89365  89371 

783 

89376  89382  89387  89393  89  398 

89404  89409 

89415  89421  89426 

784 

89432  89437  89  443  89448  89454 

89459  89465 

89470  89476  89481 

785 

89487  89492  89498  89  504  89  509 

89  515  89  520 

89  526  89  531  89537 

786 

89  542  89  548  89  553  89  559  89  564 

89  570  89  575 

89  581  89  586  89  592 

787 

89  597  89  603  89  609  89  614  89620 

89625  89631 

89636  89642  89647 

788 

89653  89  658  89  664  89669  89  675 

89680  89  686 

89691  89  697  89  702 

789 

89  708  89  713  89  719  89  724  89  730 

89  735  89  741 

89  746  89  752  89  757 

790 

89  763  89  768  89  774  89  779  89  785 

89790  897% 

89  801  89807  89812 

791 

89  818  89823  89  829  89  834  89  840 

89  845  89  851 

89  856  89  862  89867 

792 

89  873  89  878  89  883  89  889  89  894 

89900  89905 

89911  89916  89922 

793 

89927  89  933  89  938  89944  89949 

89955  89960 

89966  89971  89977 

794 

89982  89988  89  993  89998  90004 

90009  90015 

90020  90026  90031 

795 

90037  90042  90048  90053  90059 

90064  90069 

90075  90080  90086 

7% 

90091  90097  90102  90108  90113 

90119  90124 

90129  90135  90140 

797 

90146  90151  90157  90162  90168 

90173  90179 

90184  90189  90195 

798 

90200  90206  90211  90217  90222 

90  227  90  233 

90238  90244  90249 

799 

90255  90260  90266  90271  90276 

90282  90  287 

90293  90  298  90304 

800 

90309  90314  90320  90325  90331 

90336  90342 

90347  90352  90358 

N 

0    12    3    4 

5    6 

7    8    9 

.1, 


760-800 


ill 


16 

800-850 

N 

O 

1 

2 

3 

4 

5 

6 

7 

8 

9 

80O 

90309 

90314 

90320 

90  325 

90331 

90336 

90  342 

90  347 

90  352 

90  358 

801 

90363 

90  369 

90  374 

90  380 

90  385 

90390 

903% 

90  401 

90  407 

90  412 

802 

90417 

90423 

90428 

90434 

90439 

90  445 

90450 

90  455 

90  461 

90  466 

803 

90472 

90477 

90482 

90488 

90493 

90499 

90  504 

90  509 

90  515 

90  520 

804 

90  526 

90  531 

90  536 

90  542 

90  547 

90553 

90  558 

90  563 

90  569 

90  574 

805 

90  580 

90  585 

90  590 

90  5% 

90601 

90607 

90612 

90617 

90623 

90628 

806 

90634 

90  639 

90  644 

90  650 

90655 

90  660 

90666 

90  671 

90  677 

90682 

807 

90687 

90  693 

90698 

90  703 

90  709 

90  714 

90  720 

90  725 

90  730 

90  736 

808 

90  741 

90  747 

90  752 

90  757 

90  763 

90  768 

90  773 

90  779 

90  784 

90  789 

809- 

90  79i 

90800 

90  806 

90  811 

90  816 

90  822 

90827 

90  832 

90  838 

90  843 

810 

90849 

90  854 

90859  90  86i 

90  870 

90875 

90  881 

90  886 

90891 

90897 

811 

90  902 

90  907 

90  913 

90  918 

90  924 

90  929 

90  934 

90940 

90  945 

90950 

812 

90956 

90  %1 

90966 

90  972 

90  977 

90982 

90988 

90993 

90  998 

91004 

813 

91009 

91014 

91020 

91025 

91030 

91036 

91041 

91046 

91052 

91057 

814 

91062 

91068 

91073 

91078 

91084 

91089 

91094 

91100 

91105 

91110 

815 

91116 

91121 

91126 

91132 

91137 

91142 

91148 

91153 

91158 

91164 

816 

91169 

91174 

91 180  91 185 

91190 

911% 

91201 

91206 

91212 

91217 

817 

91222 

91228 

91233 

91238 

91243 

91249 

91254 

91259 

91265 

91270 

818 

91275 

91281 

91286 

91291 

91297 

91302 

91307 

91312 

91318 

91323 

819 

91328 

91334 

91339 

91344 

91350 

91355 

91360 

91365 

91371 

91376 

820 

91381 

91387 

91392 

91397 

91403 

91408 

91413 

91418 

91424 

91429 

821 

91434 

91440 

91445 

91450 

91455 

91461 

91466 

91471 

91477 

91482 

822 

91487 

91492 

91498 

91503 

91508 

91514 

91519 

91524 

91  529  91  535  1 

823 

91540 

91545 

91551 

91556 

91561 

91566 

91572 

91577 

91582 

91587 

824 

91593 

91598 

91603 

91609 

91614 

91619  91624  91630  91635 

91640 

825 

91645 

91651 

91656 

91661 

91666 

91672 

91677 

91682 

91687 

91693 

826 

91698 

91703 

91709 

91714 

91719 

91724 

91  730  91  735 

91740 

91745 

827 

91751 

91756 

91761 

91766 

91772 

91777 

91782 

91787 

91793 

91798 

828 

91803 

91808 

91814 

91819 

91824 

91829 

91834 

91840 

91845 

91850 

829 

91855 

91861 

91866 

91871 

91876 

91  882  91  887 

91892 

91897 

91903 

830 

91908 

91913 

91918 

91924 

91929 

91934 

91939 

91944 

91950 

91955 

831 

91960 

91  %5 

91971 

91976 

91981 

91  986 

91991 

91997 

<92  002^ 

92  007 

832 

92  012 

92  018 

92  023 

92  028 

92  033 

92  038 

92  044 

92  049  92  054 

92  059 

833 

92  065 

92  070 

92  075 

92  080 

92  085 

92  091 

92  0% 

92101 

92106 

92111 

834 

92117 

92122 

92127 

92132 

92137 

92143 

92148 

92153 

92158 

92163 

835 

92169 

92174 

92179 

92184 

92189 

92195 

92  200 

92  205 

92  210 

92  215 

836 

92  221 

92  226 

92  231 

92  236 

92  241 

92  247 

92  252 

92  257 

92  262 

92  267 

837 

92  273 

92  278 

92  283 

92  288 

92  293 

92  298 

92  3M 

92  309 

92  314 

92  319 

838 

92  324 

92  330 

92  335 

92  340 

92  345 

92  350 

92  355 

92  361 

92  366 

92  371 

839 

92  376 

92  381 

92  387 

92  392 

92  397 

92  402 

92  407 

92  412 

92  418 

92  423 

840 

92  428 

92  433 

92  438 

92  443 

92  449 

92  454 

92  459 

92  464 

92  469 

92  474 

841 

92  480 

92  485 

92  490 

92  495 

92  500 

92  505 

92  511 

92  516 

92  521 

92  526 

842 

92  531 

92  536 

92  542 

92  547 

92  552 

92  557 

92  562 

92  567 

92  572 

92  578 

843 

92  583 

92  588 

92  593 

92  598 

92  603 

92  609 

92  614 

92  619 

92  624 

92  629 

844 

92  634 

92  639 

92  645 

92  650  92  655 

92  660 

92  665 

92  670 

92  675 

92  681 

845 

92  686 

92  691 

92  6% 

92  701 

92  706 

92  711 

92  716 

92  722 

92  727 

92  732 

846 

92  737 

92  742 

92  747 

92  752 

92  758 

92  763 

92  768 

92  773 

92  778 

92  783 

847 

92  788 

92  793 

92  799 

92  804 

92  809 

92  814 

92  819 

92  824 

92  829 

92  834 

848 

92  840 

92  845 

92  850 

92  855 

92  860 

92  865 

92  870 

92  875 

92  881 

92  886 

849 

92  891 

92  8% 

92  901 

92  906 

92  911 

92  916 

92  921 

92  927 

92  932 

92  937 

850 

92  942 

92  947 

92  952 

92  957 

92  %2 

92  %7 

92  973 

92  978 

92983 

92  988 

N 

O 

1 

2 

3 

4 

5 

6 

7 

8 

9 

800-860 


850-900 


17 


N 

O 

1 

2 

3 

4 

5    6 

7 

8 

9 

850 

92  942 

92  947 

92  952 

92  957 

92  %2 

92  %7  92  973 

92  978 

92  983 

92  988 

851 

92  993 

92  998 

93  003 

93  008 

93  013 

93  018  93  024 

93  029 

93  034 

93  039 

852 

93  044 

93  049 

93  054 

93  059 

93  064* 

93  069  93  075 

93  080  93  085 

93  090 

853 

93  095 

93  100 

93105 

93110 

93  115 

93120  93  125 

93  131 

93  136 

93141 

854 

93146 

93151 

93156 

93  161 

93  166 

93171  93176 

93181 

93186 

93192 

855 

93197 

93  202 

93  207 

93  212 

93  217 

93  222  93  227 

93  232 

93  237 

93  242 

856 

93  247 

93  252 

93  258 

93  263 

93  268 

93  273  93  278 

93  283 

93  288 

93  293 

857 

93  298 

93  303 

93  308 

93  313 

93  318 

93  323  93  328 

93  334 

93  339 

93  344 

858 

93  349 

93  354 

93  359 

93  364 

93  369 

93  374  93  379 

93  384 

93  389 

93  394 

859 

93  399 

93  404 

93  409 

93  414 

93  420 

93  425  93  430 

93  435 

93  440 

93  445 

860 

93  450  93  455 

93  460 

93  465 

93  470 

93  475  93  480 

93  485 

93  490 

93  495 

861 

93  500 

93  505 

93  510 

93  515 

93  520 

93  526  93  531 

93  536 

93  541 

93  546 

862 

93  551 

93  556 

93  561 

93  566 

93  571 

93  576  93  581 

93  586 

93  591 

93  5% 

863 

93  601 

93  606 

93  611 

93  616 

93  621 

93  626  93  631 

93  636 

93  641 

93  646 

864 

93  651 

93  656 

93  661 

93  666 

93  671 

93  676  93  682 

93  687 

93  692 

93  697 

865 

93  702 

93  707 

93  712 

93  717 

93  722 

93  727  93  732 

93  737 

93  742 

93  747 

866 

93  752 

93  757 

93  762 

93  767 

93  772 

93  777  93  782 

93  787 

93  792 

93  797 

867 

93  802 

93  807 

93  812 

93  817 

93  822 

93  827  93  832 

93  837 

93  842 

93  847 

868 

93  852 

93  857 

93  862 

93  867 

93  872 

93  877  93  882 

93  887 

93  892 

93  897 

869 

93  902 

93  907 

93  912 

93  917 

93  922 

93  927  93  932 

93  937 

93  942 

93  947 

870 

93  952 

93  957 

93  962 

93  967 

93  972 

93  977  93  982 

93  987 

93  992 

93  997 

871 

94  002 

94  007 

94  012 

94  017 

94  022 

94  027  94  032 

94  037 

94  042 

94047 

872 

94052 

94  057 

94  062 

94  067 

94  072 

94  077  94  082 

94  086 

94  091 

940% 

873 

94101 

94106 

94111 

94116 

94121 

94126  94131 

94136 

94141 

94146 

874 

94151 

94156 

94  161 

94166 

94171 

94176  94181 

94186 

94191 

941% 

875 

94  201 

94  206 

94  211 

94  216 

94  221 

94  226  94  231 

94  236 

94  240 

94  245 

876 

94  250 

94  255 

94  260 

94  265 

94  270 

94  275  94  280 

94  285 

94  290 

94  295 

877 

94  300 

94  305 

94  310 

94  315 

94  320 

94  325  94  330  94  335 

94  340 

94  345 

878 

94  349 

94  354 

94  359 

94  364 

94  369 

94  374  94379 

94  384 

94  389 

94  394 

879 

94  399 

94  404 

94  409 

94  414 

94  419 

94  424  94  429 

94  433 

94  438 

94  443 

880 

94  448 

94  453 

94  458 

94  463 

94  468 

94  473  94  478 

94  483 

94  488 

94  493 

881 

94  498 

94  503 

94  507 

94  512 

94  517 

94  522  94  527 

94  532 

94  537 

94  542 

882 

94  547 

94  552 

94  557 

94  562 

94  567 

94  571  94  576 

94  581 

94  586 

94  591 

883 

94  5% 

94  601 

94  606 

94  611 

94  616 

94  621  94  626 

94  630 

94 1635 

9r640 

884 

94  645 

94  650 

94  655 

94  660 

94  665 

94  670  94675 

94  680 

94685 

94689 

885 

94  694 

94  699 

94  704 

94  709 

94  714 

94  719  94  724 

94  729 

94  734 

94  738 

886 

94  743 

94  748 

94  753 

94  758 

94  763 

94  768  94  773 

94  778 

94  783 

94  787 

887 

94  792 

94  797 

94  802 

94  807 

94  812 

94  817  94  822 

94  827 

94  832 

94  836 

888 

94  841 

94  846 

94  851 

94  856 

94  861 

94  866  94  871 

94  876 

94  880 

94  885 

889 

94  890 

94  895 

94  900 

94  905 

94  910 

94  915  94919 

94  924 

94929 

94  934 

890 

94  939 

94  944 

94  949 

94  954 

94  959 

94963  94968 

94973 

94  978 

94  983 

891 

94  988 

94  993 

94  998 

95  002 

95  007 

95  012  95  017 

95  022 

95  027 

95  032 

892 

95  036 

95  041 

95  0^ 

95  051 

95  056 

95  061  95  066 

95  071 

95  075 

95  080 

893 

95  085 

95  090 

95  095 

95  100 

95  105 

95  109  95  114 

95119 

95  124 

95129 

894 

95  134 

95139 

95143 

95148 

95153 

95158  95  163 

95168 

95173 

95177 

895 

95182 

95187 

95  192 

95197 

95  202 

95  207  95  211 

95  216 

95  221 

95  226 

896 

95  231 

95  236 

95  240 

95  245 

95  250 

95  255  95  260 

95  265 

95  270 

95  274 

897 

95  279 

95  284 

95  289 

95  294 

95  299 

95  303  95  308 

95  313 

95  318 

95  323 

898 

95  328 

95  332 

95  337 

95  342 

95  347 

95  352  95  357 

95  361 

95  366 

95  371 

899 

95  376 

95  381 

95  386 

95  390 

95  395 

95  400  95  405 

95  410 

95  415 

95  419 

900 

95  424 

95  429 

95  434 

95  439 

95  444 

95  448  95  453 

95  458 

95  463 

95  468 

N 

O 

1 

2 

3 

4 

5    6 

7 

8 

9 

ill 


860-900 


18 


900-960 


960-1000 


19 


|i^ 


r 


N 

O         1         2         3         4 

5 

6 

7         8         9 

900 

95  424  95  429  95  434  95  439  95  444 

95  448 

95  453 

95  458  95  463  95  468 

901 

95  472  95  477  95  482  95  487  95  492 

95  497 

95  501 

95  506  95  511  95  516 

902 

95  521  95  525  95  530  95  535  9*5  540 

95  545 

95  550 

95  554  95  559  95  564> 

903 

95  @)  95  574  95  578  95  583  95  588 

95  593 

95  598 

95  602  95  607  95  612 

904 

95  617  95  622  95  626  95  631  95  636 

95  641 

95  6*6 

95  650  95  655  95  660 

905 

95  665  95  670  95  674  95  679  95  684 

95  689 

95  694 

95  698  95  703  95  708 

906 

95  713  95  718  95  722  95  727  95  732 

95  737 

95  742 

95  746  95  751  95  756 

907 

95  761  95  766  95  770  95  775  95  780 

95  785 

95  789 

95  794  95  799  95  804 

908 

95  809  95  813  95  818  95  823  95  828 

95  832 

95  837 

95  842  95  847  95  852 

909 

95  856  95  861  95  866  95  871  95  875 

95  880 

95  885 

95  890  95  895  95  899 

910 

95  904  95  909  95  914  95  918  95  923 

95  928 

95  933 

95  938  95  942  95  947 

911 

95  952  95  957  95  %1   95  966  95  971 

95  976 

95  980 

95  985  95  990  95  995 

912 

95  999  %004  %009  %014  96019 

%023 

%028 

%033  %038  %042 

913 

%0f7  %052  %057  %061  %066 

96  071 

%076 

%080  %085  96090 

914 

96095  %099  96104  %109  %  114 

%118 

%123 

%128  %133  96137 

915 

%142  96147  %152  %  156  96161 

96166 

%171 

%175  %180  96185 

916 

%190  %194  %199  96  20*  96  209 

%213 

96  218 

%223  %227  96  232 

917 

%237  96242  %246  96251  %256 

%261 

%265 

%270  96  275   96  280 

918 

%284  %289  %294  %  298  96303 

%308 

%313 

96  317  %322  %327 

919 

96332  %336  %341  %346  %350 

%355 

%360  96365  %369  96374    | 

920 

96379  96384  %388  %393  96398 

96402 

%407 

%412  96417  %421 

921 

96426  %431  %435  %440  96445 

%450  96454 

%459  %464  96468 

922 

%473  96478  %483  %487  %492 

%497 

96  501 

96  506  %511  %515 

923 

%520  96  525  %530  %534  %539 

%544 

96  548 

%553  96  558  %562 

924 

96567  %572  %577  96  581  %586 

96  591 

96  595 

96600  96605  96609 

925 

96614  %619  %624  %628  %633 

%638 

96642 

96647  %652  96  656 

926 

%661  %666  %670  96675  96680 

%685 

%6S9 

96694  96699  %703 

927 

%708  %713  %717  96  722  %727 

%731 

%736 

96  741  %745  %750 

928 

%755  %759  %764  %769  %774 

%778 

%783 

96  788  96  792  96  797 

929 

%802  %806  %811  %816  %820 

96825  %830  9^834  %839  %844    | 

930 

%848  %853  %858  96862  %867 

%872 

%876 

96  881  96  886  %890 

931 

%895  %900  %904  96909  %914 

%918 

%923 

%928  96932  %937 

932 

%942  %946  %951  96956  %960 

96  %5 

96970 

%974  96979  %984 

933 

96988  %993  %997  97  002  97007 

97  011 

97  016 

97  021  97  025  97  030 

934 

97035  97039  97044  97  0*9  97  053 

97058 

97  063 

97  067  97  072  97  077 

935 

97  081  97086  97090  97095  97100 

97104 

97109 

97114  97118  97123 

936 

97128  97132  97137  97142  97146 

97151 

97155 

97160  97165  97169 

937 

97174  97179  97183  97188  97192 

97197 

97  202 

97  206  97  211  97  216 

938 

97  220  97  225   97  230  97  234  97  239 

97  243 

97  248 

97  253  97  257  97  262 

939 

•97  267  97  271   97  276  97  280  97  285 

97  290 

97  294 

97  299  97  30*  97  308 

940 

97  313  97  317  97  322  97  327  97331 

97  336 

97  340 

97  345  97  350  97  354 

9*1 

97  359  97  364  97368  97  373  97  377 

97  382 

97  387 

97  391   97  396  97  400 

942 

97  405  97  410  97  414  97  419  97  424 

.  97428 

97  433 

97  437  97442  97  447 

943 

97  451  97  456  97  460  97  465  97  470 

97  474 

97479 

97  483  97  488  97493 

944 

97  497  97  502  97  506  97  511  97  516 

97  520 

97  525 

97  529  97  534  97  539 

945 

97  543  97  548  97  552  97  557  97  562 

97  566 

97  571 

97  575  97  580  97  585 

946 

97  589  97  594  97  598  97  603  97  607 

97  612 

97  617 

97621   97  626  97  630 

947 

97  635  97  640  97  644  97  649  97653 

97  658 

97  663 

97  667  97  672  97  676 

948 

97  681   97  685  97  690  97  695  97  699 

97  704 

97  708 

97  713  97  717  97  722 

949 

97  727  97  731  97  736  97  740  97  745 

97  749 

97  754 

97  759  97  763  97  768 

950 

97  772  97  777  97  782  97  786  97  791 

97  795 

97  800 

97  80*  97  809  97  813 

N 

O         1          2         3         4 

5 

6 

7         8         9 

N 

o 

1 

2         3         4 

5         6         7         8         9 

950 

97  772 

97  777 

97  782  97  786  97  791 

97  795  97  800  97  804  97  809  97  813 

951 

97  818 

97  823 

97  827  97  832  97  836 

97  841  97  845  97  850  97  855  97  859 

952 

97  864 

97  868 

97  873  97  877  97  882 

97  886  97  891  97  896  97  900  97  905 

953 

97  909 

97  914 

97  918  97  923  97  928 

97  932  97  937  97941  97946  97950 

954 

97955  97959  97964  97968  97  973 

•97  978  97  982  97  987  97  991  97  9% 

955 

98000 

98005 

98009  98014  98019 

98  023  98028  98032  98037  98041 

956 

98046  98050  98055  98059  98  06* 

98068  98073  98078  98082  98087 

957 

98091 

98096 

98100  98105  98109 

98114  98118  98123  98127  98132 

958 

98137 

98141 

98146  98150  98155 

98159  98164  98168  98173  98177 

959 

98182 

98186 

98191  98195  98  200 

98  204  98209  98  214  98  218  98  223 

960 

98  227 

98  232 

98  236  98  241  98  245 

98  250  98  254  98  259  93  263  98  268 

961 

98  272 

98  277 

98  281  98  286  98  290 

98  295  98  299  98  304  98  308  98  313 

%2 

98318 

98322 

98327  98331  98  336 

98340  98  345  98349  98  354  98  358 

%3 

98  363 

98  367 

98372  98376  98381 

98385  98390  98394  98  399  98  403 

964 

98408 

98  412 

98417  98421  98426 

98  430  98435  98439  98444  98448 

965 

98453 

98457 

98462  98466  98471 

98  475  98480  98484  98489  98493 

966 

98  498 

98  502 

98  507  98  511  98  516 

98  520  98  525  98  529  98  534  98  538 

%7 

98  543 

98  547 

98  552  98  556  98  561 

98  565  98  570  98  574  98  579  98  583 

968 

98  588 

98  592 

98  597  98  601  98605 

98610  98  614  98619  98  623  98628 

%9 

98632 

98637 

98641  98646  98650 

98655  98659  98664  98668  98673 

970 

98677 

98682 

98  686  98  691  98695 

98  700  98  704  98  709  98  713  98  717 

971 

98  722 

98  726 

98  731  98  735  98  740 

98  744  98  749  98  753  98  758  98  762 

972 

98  767 

98  771 

98  776  98  780  98  784 

98  789  98  793  98  798  98  802  98  807 

973 

98  811 

98  816 

98  820  98  825   98  829 

98834  98  838  98  843  98  847  98  851 

974 

98856  98860  98  865  98869  98  874 

98878  98  883  98887  98892  98  8% 

975 

98900 

98905 

98909.98914  98918 

98923  98927  98  932  98936  98941 

976 

98945 

98949 

98954  98958  98  963 

98  %7 '98  972  98976  98981  98985 

977 

98989 

98  994 

98998  99003  99007 

99012  99  016  99021   99025   99029 

978 

99034 

99038 

990*3  99047  99052 

99056  99061   99065   99069  99074 

979 

99078 

99083 

99087  99092  99096 

99100  99105  99109  99114  99118 

980 

99123 

99127 

99131  99136  99140 

99145  99149  99154  99158  99162 

981 

99167 

99171 

99176  99180  99185 

99189  99193  99198  99  202  99  207 

982 

99  211 

99  216 

99  220  99  224  99  229 

99  233  99  238  99  242  99  247  99  251 

983 

99  255 

99  260 

99  264  99  269  99  273 

99  277  99  282  99  286  99  291  99  295 

984 

99300 

99  30* 

99308  99313  99  317 

99322  99  326  99  330  99335  99339 

985 

99344 

99348 

99  352  99357  99361 

99366  99  370  99374  99379  99383 

986 

99388 

99392 

99  396  99401  99405 

99410  99414  99  419  99  423  99427 

987 

99432 

99  436 

99441  99445   99449 

99454  99458  99463  99  467  99471 

988 

99476 

99  480 

99484  99  489  99  493 

99  498  99  502  99  506  99  511   99  515 

989 

99  520 

99  524 

99  528  99  533  99  537 

99  542  99  546  99  550  99  555  99  559 

990 

99  564 

99  568 

99  572  99  577  99  581 

99  585   99590  99  594  99  599  99603 

991 

99607 

99612 

99  616  99  621   99  625 

99629  99634  99638  99642  99647 

992 

99651 

99656 

99660  99664  99669 

99673  99677  99682  99686  99691 

993 

99695 

99699 

99  704  99  708  99  712 

99717  99  721  99  726  99  730  99  734 

994 

99  739 

99  743 

99  747  99  752  99  756 

99  760  99  765  99  769  99  7>4  99  778 

995 

99  782 

99  787 

99  791  99  795  99800 

99804  99  808  99  813  99  817  99  822 

9% 

99826 

99  830 

99  835  99  839  99  843 

99848  99852  99856  99861  99865 

997 

99  870 

99  874 

99878  99  883  99  887 

99891  998%  99900  99904  99909 

998 

99913 

99  917 

99  922  99  926  99  930 

99935  99939  99944  99948  99952 

999 

99957 

99961 

99  %5  99970  99  974 

99978  99983  99987  99991  999% 

lOOO 

00000 

00004 

00009  00013  00017 

00022  00026  00030  00035  00039 

N 

O 

1 

2         3         4 

5         6         7         8         9 

900-960 


960-1000 


20     TABLE  IL-LOGAEITHMS  OF  CONSTANTS. 


i 

I 


I 

J  T    ' 


Circumference  of  the  Circle  in  decrees =           360 

log 

2.55  630250 
4.33  445  375 
6.11260  500 

0.49  714987 

Circumference  of  the  Circle  in  minutes =      21  600 

Circumference  of  the  Circle  in  seconds =1  296  000 

If  the  radius  r  =  1,  half  the  Circumference  of  the  Circle  is 
IT  —  3. 14  159  265  358  979  323  846  264  338  ^^S 

Also  : 
2x=   6.28  318  531 

4  Tr  =  12.  56  637  061 

^=    1.57079633 
2 

^=    1.04  719  755 
3 

^''=    4.18  879020 
3 

^=   0.78539816 

^=   0.52  359878 
6 

i=   0.31830989 

w 

~=   0.15  915  494 

1=    0.95492966 

-=    1.27323  954 

^  =   0.23  873  241 
4-^ 

log 
0.79817  987 

1.09920986 

0.19611988 

0.02  002  862 

0.62  208861 

9.89  508988-10 

9.71899862-10 

9.50  285  013-10 

9.20182013-10 

9.97997138-10 

0.10491012 

9.37  791139-10 

t8  =  9.  86960  440 
1  =  0. 10  132  lis 

Vt  =  1.77  245  385 
^    =0.56418958 

J?  =  0. 97  720  502 

^  =  1.12837917 

^T  =  1.46  459  189 
^    =0.68278406 

^ir2  =  2.14  502  940 
l\^  =0.62035  049 

i/?  =  0.  80  599  598 

log 
0.99429  975 

9.00  570025-10 

0.24  857494 
9.75142  506-10 

9.98998  569-10 

0.05  245  506 

0.16  571662 
9.83  428338-10 

0.33143  325 
9.79263  713-10 

9.90633  287-10 

Arc  a,  whose  length  is  equal  to  the  radius  r,  is  : 

in  degrees a° =  ^^ =  57.29577 95 1°. 

in  minutes a' _  10  800 _  ,  ^^^  j^  ^^^, 

log 

1.  75  812  263 

3.53  627  388 
5.31442  513 

2.05  915  263 
3.83  730388 
5.61545  513 

8. 24  187  737  -  10 
6.46372  612-10 
4.68  557487-10 
7.94  084  737-10 
6.16269612-10 

4.38  454487-10 
4.68557487-10 

in  seconds 

Arc  2  a,  whose  lengt 
in  degrees 

In  minutes 

in  seconds 

If  the  radius  r  =  1,  i 
for  1  degree . . . 

for  1  minute . . . 

.a" =  648  000 =  206264.806".. 

IT 

h  is  equal  to  twice  the  radius,  2  r,  is  : 

.  2  ao  . . . .  =  ^^ =  114.  59  155  903° 

w 

.2a'  ....  =  ^^^^ =  6875.49354'.. 

w 

.  2  a" . . . .  =  ^  ^^  ^^  . . .  =  412  529. 612"  . . 

m 

the  length  of  the  arc  is : 

. .  ^ -   ""   -  0. 01  745  329. . . 

a°               180 

fnr  1  Rpfiond 

a' 10800" 

1                            ir 

....  =  0.00000485... 

.   ..  =  0.0087266i... 

—  0  00  014  544. . . 

for  \  degree  . . . 

for  J  minute. . . 

for  J  second . . . 
Sin  1"  in  the  unit  ci 

•    •    "        ■  •   •   •  •   «   —                         -  .  .  .    ^ 

a"              648  000 

1                              IT 

**2a°   ""      860'*" 

1                          ir 

"2a' 21600* 

1                     » 

-....  =  0.00000242... 
J 

--..  =  0.00000485... 

"2a'i""      129600( 
rcle 

21 


tf 


O 

1 

2 
3 

4 

5 

6 

7 
8 
9 

lO 

11 
12 
13 
14 

16 

16 
17 
18 
19 

20 

21 
22 
23 
24 

25 

26 
27 
28 
29 

ao 


ft 


TABLE  m. 


THE  LOGAEITHMS 


OF  THE 


TRIGOIN^OMETRIC  FTJNCTIOIS^S : 

Prom  (f  to  0°  3',  or  89°  57'  to  90°,  for  every  second ; 
From  0°  to  2°,  or  88°  to  90°,  for  every  ten  seconds ; 
Prom  1°  to  89°,  for  every  minute. 


Note.    To  all  the  logarithms  — 10  is  to  be  appended. 


log  sin 


0' 


log  tan  =  log  sin 
log  cos  =  10.  GO  000 


O' 


1' 


2' 


4. 68  557 
4.98  660 
5.16  270 
5.  28  763 

5.38454 
5.46373 
5.  53  067 
5.58  866 
5. 63  982 

5.68  557 
5.  72  697 
5.76  476 
5.79952 
5. 83  170 

5. 86 167 
5.88%9 
5. 91  602 
5.94  085 
5.96433 

5.98  660 
6. 00  779 
6. 02  800 
6.04  730 
6.06  579 

6.08  351 
6.10055 
6. 11  694 

6. 13  273 

6. 14  797 


6.46  373 

6.47  090 
6. 47  797 
6.  48  492 
6.49175 

6.49  849 

6.50  512 
6.  51 165 
6.  51  808 
6.  52  442 

6.  53  067 
6.  53  683 
6.  54  291 
6.  54  890 
6.  55  481 

6.56064 
6.  56  639 
6.  57  207 
6.  57  767 
6.58320 

6.  58  866 
6.59  406 
6.59939 
6.60465 
6.60985 

6.  61  499 
6.62  007 

6. 62  509 

6.63  006 
6.63  4% 


6.76476 
6.  76  836 
6.  77  193 
6.  77  548 
6.77  900 

6.  78  248 
6.  78  595 
6.78938 
6.  79  278 
6.79616 

6.79  952 

6.80  285 
6.80615 
6.80943 

6. 81  268 

6. 81  591 
6.  81  911 

6. 82  230 
6.  82  545 
6.  82  859 

6.  83  170 
6.  83  479 

6. 83  786 

6.84  091 
6.84  394 

6.84  694 
6.84  993 
85  289 
85  584 
85  876 


tf 


6.16  270    6.63  982    6.86167 


69' 


68' 


67' 


eo 

59 

58 
57 
56 

55 

54 
53 
52 
51 

50 

49 

48 
47 
46 

45 

44 
43 
42 
41 

40 

39 
38 
37 
36 

35 

34 
33 
32 
31 

30 


tf 


ff 


30 

31 
32 
ZZ 
34 

36 

36 
37 
38 
39 

40 

41 
42 
43 
44 

45 

46 
47 
48 
49 

60 

51 
52 
53 
54 

55 

56 

57 
58 
59 

60 


O' 


1' 


2' 


ff 


6. 16  270 

6.17  694 
6.19072 
6.20  409 

.6.21705 

6.22  964 
6.  24  188 
6.  25  378 
6.  26  536 
6.27  664 

6.  28  763 
6.  29  836 
6;  30  882 
6.31904 

6.32  903 

6. 33  879 

6. 34  833 

6. 35  767 
6.36682 

6.37  577 

6.38  454 

6. 39  315 

6. 40  158 
6.40985 

6. 41  797 

6.42  594 

6.43  376 

6.44145 

6.44  900 

6. 45  643 


6. 63  982 

6. 64  462 

6.64  936 

6.65  406 
6.  65  870 

6.66330 

6. 66  785 

6. 67  235 

6.67  680 
6.  68  121 

6. 68  557 
6.68990 
6.69418 

6.69  841 
6.  70  261 

6.70676 
6.  71  088 
6.  71  4% 
6.71900 
6.  72  300 

6.  72  697 

6.73  090 
6.  73  479 
6.  73  865 
6.  74  248 

6.74  627 
6.  75  003 
6.  75  376 
6.  75  746 
6.  76 112 


6.  86  167 
6.86455 

6. 86  742 

6.87  027 
6.87310 

6.87  591 

6. 87  870 

6. 88  147 

6. 88  423 
6.88697 

6.88969 
6.  89  240 

6.89  509 
6.  89  776 

6.90  042 

6.90306 

6.90  568 
6.  90  829 

6. 91  088 
6. 91  346 

6.  91  602 

6. 91  857 

6. 92  110 
6. 92  362 
6.92  612 

6. 92  861 

6. 93  109 
6. 93  355 
6. 93  599 
6. 93  843 


6.46373    6.76476   6.94  085 


69' 


58' 


57' 


ft 


log  cot  =  log  COS 

log  sin  =  10. 00  000 


30 

29 
28 
27 
26 

25 

24 
23 
22 
21 

20 

19 
18 
17 
16 

15 

14 
13 
12 
11 

lO 

9 
8 
7 
6 

6 

4 
3 
2 
1 

O 


r9 


89' 


log  cos 


I 


fl 


it  [ 


22 

OP 

\ 

t  ff 

log  sin 

log  tau 

log  COS 

ff   * 

f  ff 

log  sin 

7. 46  373 

log  tan 

log  COS 

ff  f 

O    0 

— 

_^ 

10.00000 

0  6O 

lOO 

7. 46  373 

10.00000 

0  5O 

10 

5.68  557 

5. 68  557 

10.00000 

50 

10 

7.47  090 

7. 47  091 

10.00000 

50 

20 

5.98660 

5.98660 

10.00000 

40 

20 

7.47  797 

7. 47  797 

10.00000 

40 

30 

6.16  270 

6. 16  270 

10.00000 

30- 

30 

7. 48  491 

7.  48  492 

10.00000 

30 

40 

6. 28  763 

6.  28  763 

10.00000 

20 

40 

7. 49  175 

7.49176 

10.00000 

20 

50 

6.38  454 

6.  38  454 

10.00000 

10 

50 

7.49  849 

7.49  849 

10.00000 

10 

1     0 

6.46373 

6.  46  373 

10.00000 

059 

110 

7.50  512 

7.50512 

10.00000 

049 

10 

6.  53  067 

6.  53  067 

10.00000 

50 

10 

7.51165 

7.  51 165 

10.00000 

50 

20 

6.58  866 

6.58  866 

10.00000 

40 

20 

7.51808 

7.51809 

10.00000 

40 

30 

6.63  982 

6.63  982 

10.00000 

30 

30 

7.52  442 

7.52  443 

10.00000 

30 

40 

6.  68  557 

6. 68  557 

10.00000 

20 

40 

7.  53  067 

7.53  067 

10.00000 

20 

50 

6.72  697 

6.  72  697 

10.00000 

10 

50 

7.53  683 

7.  53  683 

10.00000 

10 

2    0 

6.76476 

6.76476 

10.00000 

058 

12  0 

7.  54  291 

7.54  291 

10.00000 

048 

10 

6.79952 

6.79952 

10.00000 

50 

10 

7.  54  890 

7.  54  890 

10.00000 

50 

20 

6.83170 

6. 83  170 

10.00000 

40 

20 

7.  55  481 

7. 55  481 

10.00000 

40 

30 

6.  86  167 

6. 86  167 

10.00000 

30 

30 

7.56064 

7.56064 

10.00000 

30 

40 

6.88%9 

6.  88  %9 

10.00000 

20 

40 

7.56639 

7.56639 

10.00000 

20 

50 

6.91602 

6.  91  602 

10.00000 

10 

50 

7.  57  206 

7.57  207 

10.00000 

10 

3    0 

6.94085 

6.94085 

10.00000 

057 

13  0 

7.  57  767 

7.  57  767 

10.00000 

047 

10 

6.%  433 

6.96433 

10.00000 

50 

10 

7.58320 

7.58  320 

10.00000 

50 

20 

6.98  660 

6.98661 

10.00000 

40 

20 

7.58866 

7.58  867 

1000000 

40 

30 

7. 00  779 

7.00  779 

10.00000 

30 

30 

7.59406 

7.59406 

10.00000 

30 

40 

7.02  800 

7.02  800 

10.00000 

20 

40 

7.59939 

7.59939 

10.00000 

20 

50 

7.(H730 

7.  (H  730 

10.00000 

10 

50 

7.60465 

7.60466 

10.00000 

10 

4    0 

7.06  579 

7.06579 

10.00000 

056 

14  0 

7.60985 

7.60986 

10.00000 

046 

10 

7.08  351 

7.08352 

10.00000 

50 

10 

7. 61  499 

7. 61  500 

10.00000 

50 

20 

7.10055 

7.10055 

10.00000 

40 

20 

7.62  007 

7.62  008 

10.00000 

40 

30 

7.11694 

7.11694 

10.00000 

30 

30 

7. 62  509 

7.62  510 

10.00000 

30 

40 

7. 13  273 

7. 13  273 

10.00000 

20 

40 

7.63  006 

7.63  006 

10.00000 

20 

50 

7. 14  797 

7. 14  797 

10.00000 

10 

50 

7.63  4% 

7. 63  497 

10.00000 

10 

5    0 

7.16270 

7. 16  270 

10.00000 

055 

16  0 

7.63  982 

7. 63  982 

10.00000 

045 

10 

7.17  694 

7.17  6^ 

10.00000 

50 

10 

7.64  461 

7. 64  462 

10.00000 

50 

20 

7.19072 

7.19073 

10.00000 

40 

20 

7.64  936 

7.64937 

10.00000 

40 

30 

7.20409 

7.20409 

10.00000 

30 

30 

7.65  406 

7.65  406 

10.00000 

30 

40 

7.  21  705 

7. 21  705 

10.00000 

20 

40 

7.65  870 

7.65  871 

10.00000 

20 

50 

7.22  964 

7.22  96+ 

10.00000 

10 

50 

7.66330 

7.66330 

10.00000 

10 

6    0 

7.  24  188 

7.  24  188 

10.00000 

054 

16  0 

7. 66  784 

7. 66  785 

10.00000 

044 

10 

7. 25  378 

7.  25  378 

10.00000 

50 

10 

7.67  235 

7. 67  235 

10.00000 

50 

20 

7.26536 

7.26536 

10.00000 

40 

20 

7.67680 

7.67  680 

10.00000 

40 

30 

7.27  661 

7.27  664 

10.00000 

30 

30 

7.68121 

7.68121 

10.00000 

30 

40 

7. 28  763 

7.  28  764 

10.00000 

20 

40 

7.68  557 

7. 68  558 

9.99999 

20 

50 

7. 29  836 

7.29  836 

10.00000 

10 

50 

7.68989 

7.68990 

9.99999 

10 

7    0 

7.30882 

7.30882 

10.00000 

053 

170 

7.69417 

7.69418 

9.99999 

043 

10 

7.31904 

7.319(H 

10.00000 

50 

10 

7.69841 

7.69  842 

9.99  999 

50 

20 

7.32  903 

7.32  903 

10.00000 

40 

20 

7.70  261 

7.70  261 

9.99999 

40 

30 

7. 33  879 

7.33  879 

10.00000 

30 

30 

7.70676 

7.70677 

9.99  999 

30 

40 

7. 34  833 

7.34  833 

10.00000 

20 

40 

7.71088 

7.  71 088 

9.99  999 

20 

50 

7.35  767 

7. 35  767 

10.00000 

10 

50 

7.  71 496 

7.  71 4% 

9.99999 

10 

8    0 

7.36682 

7.36682 

10.00000 

052 

18  0 

7.71900 

7.71900 

9.99999 

042 

10 

7.37  577 

7.37  577 

10.00000 

50 

10 

7.72  300 

7.72  301 

9.99999 

50 

20 

7.38454 

7.38455 

10.00000 

40 

20 

7.72  697 

7.  72  697 

9.99999 

40 

30 

7.39314 

7.39315 

10.00000 

30 

30 

7.73  090 

7.73  090 

9.99999 

30 

40 

7. 40  158 

7. 40 158 

10.00000 

20 

40 

7. 73  479 

7.73  480 

9.99  999 

20 

50 

7.40985 

7.40985 

10.00000 

10 

50 

7.  73  865 

7.73  866 

9.99999 

10 

9    0 

7. 41  797 

7. 41  797 

10.00000 

0  51 

190 

7.  74  248 

7.74248 

9.99999 

041 

10 

7. 42  594 

7.42  594 

10.00000 

50 

10 

7.74  627 

7.  74  628 

9.99999 

50 

20 

7.43  376 

7.43  376 

10.00000 

40 

20 

7.  75  003 

7.75  004 

9.99  999 

40 

30 

7.44145 

7. 44  145 

10.00000 

30 

30 

7.  75  376 

7.  75  377 

9.99  999 

30 

40 

7.44900 

7.44  900 

10.00000 

20 

40 

7.  75  745 

7.  75  746 

9.99  999 

20 

50 

7.45  643 

7. 45  (AZ 

10.00000 

10 

50 

7. 76 112 

7. 76 113 

9.99  999 

10 

lOO 

7.46373 

7.46373 

10.00000 

05O 

20  0 

7.76475 

7.76476 

9.99  999 

04O 

f  ff 

log  cos 

log  cot 

log  sin 

ff  f 

f  ff 

log  cos 

log  cot 

log  sin 

ft  t 

m 


23 


f  ff 

log  sin 

log  tan 

log  COS 

9.99  999 

ff   f 

'   "    log  sin 

log  tan 

log  cos 

ft  t 

20  0 

7.76  475 

7.76476 

04O 

30  0  1  7. 94  084 

7.94  086 

9.99998 

03O 

10 

7.76836 

7.76  837 

9.99  999 

50 

10 

7.94  325 

7.94  326 

9.99998 

50 

20 

7.  77  193 

7.  77  194 

9.99999 

40 

20 

7.94  564 

7.94  566 

9.99  998 

40 

30 

7. 77  548 

7.  77  549 

9.99  999 

30 

30 

7. 94  802 

7.94  804 

9.99  998 

30 

40 

7.  77  899 

7.77900 

9.99  999 

20 

40 

7. 95  039 

7.95  040 

9.99998 

20 

50 

7.78  248 

7.78  249 

9.99  999 

10 

50 

7. 95  274 

7. 95  276 

9.99998 

10 

210 

7.  78  594 

7.  78  595 

9.99  999 

039 

310 

7.95  508 

7.95  510 

9.99  998 

0  29 

10 

7.  78  938 

7.78  938 

9.99  999 

50 

10 

7. 95  741 

7. 95  743 

9.99998 

50 

20 

7.79278 

7.79  279 

9.99  999 

40 

20 

7. 95  973 

7.95  974 

9.99998 

40 

30 

7.79  616 

7.79  617 

9.99  999 

30 

30 

7.  %  203 

7.96  205 

9.99998 

30 

40 

7.79  952 

7.79952 

9.99999 

20 

40 

7.%  432 

7.%  434 

9.99  998 

20 

50 

7.80  284 

7.80  285 

9.99999 

10 

50 

7.%660 

7.96662 

9.99  998 

10 

220 

7.80615 

7.80615 

9.99  999 

038 

32  0 

7.%  887 

7. 96  889 

9.99998 

0  28 

10 

7.  80  942 

7.80943 

9.99  999 

50 

10 

7.97113 

7.97114 

9.99  998 

50 

20 

7. 81  268 

7. 81  269 

9.99999 

40 

20 

7. 97  337 

7. 97  339 

9.99  998 

40 

30 

7. 81  591 

7. 81  591 

9.99999 

30 

30 

7. 97  560 

7.97  562 

9.99  998 

30 

40 

7.81911 

7.  81 912 

9.99  999 

20 

40 

7.  97  782 

7.97  784 

9.99  998 

20 

50 

7.  82  229 

7.  82  230 

9.99  999 

10 

50 

7.98  003 

7.98005 

9.99998 

10 

230 

7.  82  545 

7. 82  546 

9.99  999 

037 

330 

7.  98  223 

7.  98  225 

9.99998 

0  27 

10 

7. 82  859 

7.  82  860 

9.99  999 

50 

10 

7. 98  442 

7.98  444 

9.99  998 

50 

20 

7.83  170 

7.83171 

9.99999 

40 

20 

7.98  660 

7.98  662 

9.99  998 

40 

30 

7.83  479 

7.83  480 

9.99  999 

30 

30 

7.98  876 

7.98  878 

9.99  998 

30 

40 

7.83  786 

7. 83  787 

9.99  999 

20 

40 

7.99092 

7.99094 

9.99998 

20 

50 

7.84091 

7.84092 

9.99  999 

10 

50 

7.99306 

7.99  308 

9.99998 

10 

240 

7.84  393 

7.84  394 

9.99  999 

036 

340 

7.99  520 

7.99  522 

9.99  998 

0  26 

1 

10 

7. 84  694 

7.84  695 

9.99999 

50 

10 

7.99  732 

7.  99  734 

9.99  998 

50 

1 

20 

7.84  992 

7.84  994 

9.99  999 

40 

20 

7.99943 

7.99  946 

9.99998 

40 

H 

30 

7. 85  289 

7. 85  290 

9.99999 

30 

30 

8. 00 154 

8.00156 

9.99998 

30 

40 

7. 85  583 

7. 85  584 

9.99999 

20 

40 

8.00363 

8.00365 

9.99998 

20 

50 

7. 85  876 

7.  85  877 

9.99  999 

10 

50 

8.00  571 

8.00  574 

9.99998 

10 

250 

7.  86  166 

7. 86  167 

9.99  999 

035 

35  0 

8.00  779 

8. 00  781 

9.99  998 

0  25 

10 

7.86455 

7. 86  456 

9.99999 

50 

10 

8.00  985 

8.00987 

9.99  998 

50 

20 

7.  86  741 

7. 86  743 

9.99  999 

40 

20 

8.01190 

8.01193 

9.99998 

40 

30 

7.87  026 

7.87  027 

9.99  999 

30 

30 

8.01395 

8. 01  397 

9.99998 

30 

40 

7.87309 

7.87  310 

9.99999 

20 

40 

8. 01  598 

8.01600 

9.99  998 

20 

50 

7. 87  590 

7.87  591 

9.99999 

10 

50 

8.01801 

8.01803 

9.99  998 

10 

260 

7. 87  870 

7.87  871 

9.99999 

034 

360 

8.02  002 

8.02  004 

9.99998 

0  24 

10 

7. 88  147 

7. 88 148 

9.99999 

50 

10 

8. 02  203 

8. 02  205 

9.99998 

50 

20 

7.88423 

7.88424 

9.99999 

40 

20 

8. 02  402 

8.02  405 

9.99998 

40 

30 

7.88697 

7.88  698 

9.99999 

30 

30 

8.02  601 

8.02  604 

9.99998 

30 

40 

7.88  %9 

7.  88  970 

9.99  999 

20 

40 

8.  02  799 

8. 02  801 

9.99  998 

20 

50 

7. 89  240 

7.89  241 

9.99  999 

10 

50 

8.02  996 

8.02  998 

9.99998 

10 

270 

7.89  509 

7.89  510 

9.99999 

033 

37  0 

8.03192 

8.  03  194 

9.99997 

0  23 

10 

7.  89  776 

7.89  777 

9.99999 

50 

10 

8.03  387 

8. 03  390 

9.99997 

50 

20 

7.900+1 

7.90043 

9.99  999 

40 

20 

8.  03  581 

8. 03  584 

9.99997 

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1 

30 

7.90305 

7.90307 

9.99  999 

30 

30 

8.03  775 

8. 03  777 

9.99  997 

30 

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40 

7.90  568 

7.90  569 

9.99999 

20 

40 

8. 03  %7 

8. 03  970 

9.99997 

20 

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7.90829 

7.90830 

9.99  999 

10 

50 

8. 04  159 

8.04162 

9.99997 

10 

280 

7. 91 088 

7. 91 089 

9.99999 

032 

380 

8.04  350 

8.04  353 

9.99997 

0  22 

10 

7. 91  346 

7.91347 

9.99  999 

50 

10 

8.04  540 

8. 04  543 

9.99997 

50 

20 

7.  91  602 

7.91603 

9.99999 

40 

20 

8.04  729 

8. 04  732 

9.99997 

40 

30 

7.91857 

7. 91  858 

9.99  999 

30 

30 

8.04  918 

8.04  921 

9.99997 

30 

40 

7.92110 

7. 92  111 

9.99998 

20 

40 

8.05  105 

8.05  108 

9.99997 

20 

50 

7.92  362 

7.92  363 

9.99998 

10 

50 

8.05  292 

8. 05  295 

9.99997 

10 

290 

7.92  612 

7.92  613 

9.99998 

031 

39  0 

8. 05  478 

8.05  481 

9.99997 

0  21 

10 

7.92  861 

7. 92  862 

9.99998 

50 

10 

8. 05  663 

8.05  666 

9.99997 

50 

20 

7. 93  108 

7.93110 

9.99998 

40 

20 

8.05  848 

8.05  851 

9.99997 

40 

30 

7. 93  354 

7. 93  356 

9.99998 

30 

30 

8.06  031 

8.06034 

9.99  997 

30 

40 

7. 93  599 

7. 93  601 

9.99  998 

20 

40 

8.  06  214 

8.06  217 

9.99  997 

20 

50 

7.  93  842 

7. 93  844 

9.99  998 

10 

50 

8.06  3% 

8.06  399 

9.99  997 

10 

3O0 

7.94  084 

7.94086 

9.99998 

03O 

4O0 

8.06  578 

8.06  581 

9.99997 

0  2O 

• 

f  ff 

log  COS 

log  cot 

log  sin 

ff  f 

f  ff 

log  cos 

log  cot 

log  sin 

ft  t 

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11 


nil 


f  '/ 

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log  tan 

8.06  581 

log  COS      "    ' 

f  ff 

log  sin 

log  tan 

log  COS 

9.99995 

ff  f 

4O0 

8.06  578 

9.99997 

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6O0 

8.16  268 

8.16  273 

OlO 

10 

8. 06  758 

8.06  761 

9.99997 

50 

10 

8.16413 

8.16417 

9.99995 

50 

20 

8.06938 

8.06941 

9.99997 

40 

20 

8.16557 

8.16  561 

9.99995 

40 

30 

8.07  117 

8. 07  120 

9.99997 

30 

30 

8.16  700 

8.16  705 

9.99995 

30 

40 

8. 07  295 

8. 07  299 

9.99997 

20 

40 

8.16843 

8.16  848 

9.99995 

20 

50 

8.07473 

8. 07  476 

9.99997 

10 

50 

8.16986 

8.16991 

9.99995 

10 

410 

8.07  650 

8.07  653 

9.99997 

019 

610 

8. 17  128 

8. 17  133 

9.99995 

0    9 

10 

8. 07  826 

8. 07  829 

9.99997 

50 

10 

8. 17  270 

8.17  275 

9.99995 

50 

20 

8.08002 

8.0800i 

9.99997 

40 

20 

8.17  411 

8.17  416 

9.99995 

40 

30 

8. 08  176 

8.08180 

9.99997 

30 

30 

8. 17  552 

8. 17  557 

9.99995 

30 

40 

8. 08  350 

8. 08  354 

9.99997 

20 

40 

8.17  692 

8. 17  697 

9.99995 

20 

50 

8. 08  524 

8.  08  527 

9.99997 

10 

50 

8.17  832 

8.17837 

9.99995 

10 

420 

8.08  6% 

8.08  700 

9.99  997 

018 

62  0 

8.17  971 

8.17976 

9.99995 

0    8 

10 

8.08  868 

8.  08  872 

9.99  997 

50 

10 

8.18110 

8. 18  115 

9.99995 

50 

20 

8.09040 

8.09043 

9.99997 

40 

20 

8. 18  249 

8.18  254 

9.99995 

40 

30 

8.09  210 

8.09  214 

9.99  997 

30 

30 

8.18  387 

8.18  392 

9.99995 

30 

40 

8.09380 

8.09  384 

9.99997 

20 

40 

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8. 18  530 

9.99995 

20 

50 

8.09  550 

8.09  553 

9.99997 

10 

50 

8.18662 

8.18667 

9.99995 

10 

430 

8.09  718 

8.  09  722 

9.99997 

017 

63  0 

8. 18  798 

8.18  804 

9.99995 

0    7 

10 

8.09  886 

8.09  890 

9.99997 

50 

10 

8.18935 

8.18  940 

9.99995 

50 

20 

8.10054 

8.10057 

9.99997 

40 

20 

8.19071 

8.19076 

9.99995 

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30 

8. 10  220 

8.10  224 

9.99  997 

30 

30 

8.19  206 

8.19212 

9.99995 

30 

40 

8.10386 

8.10390 

9.99997 

20 

40 

8.19341 

8.19347 

9.99995 

20 

50 

8.10552 

8.10  555 

9.99  9% 

10 

50 

8.19476 

8.19481 

9.99995 

10 

440 

8. 10  717 

8. 10  720 

9.99  9% 

016 

640 

8.19610 

8. 19  616 

9.99  995 

0    6 

10 

8.10881 

8.10  884 

9.999% 

50 

10 

8.19  744 

8. 19  749 

9.99  995 

50 

20 

8.11044 

8.11048 

9.999% 

40 

20 

8.19  877 

8.19  883 

9.99995 

40 

30 

8. 11  207 

8.11211 

9.999% 

30 

30 

8.20010 

8.20016 

9.99995 

30 

40 

8.11370 

8.11373 

9.999% 

20 

40 

8.  20 143 

8.  20  149 

9.99995 

20 

50 

8. 11  531 

8. 11  535 

9.999% 

10 

50 

8.20  275 

8.20281 

9.99994 

10 

450 

8. 11 693 

8. 11  6% 

9.999% 

016 

66  0 

8.20407 

8.20413 

9.99994 

0    6 

10 

8.11853 

8.11857 

9.999% 

50 

10 

8.20  538 

8. '20  544 

9.99  994 

50 

20 

8.12  013 

8.12  017 

9.999% 

40 

20 

8.20669 

8.20  675 

9.99  994 

40 

30 

8. 12  172 

8. 12  176 

9.99  9% 

30 

30 

8.20800 

8.  20  806 

9.99994 

30 

40 

8.12  331 

8.12  335 

9.999% 

20 

40 

8.20930 

8.20936 

9.99994 

20 

50 

8.12  489 

8.12  493 

9.999% 

10 

50 

8.21060 

8.21066 

9.99994 

10 

460 

8.12647 

8.12651 

9.999% 

014 

66  0 

8. 21 189 

8. 21 195 

9.99994 

0    4 

10 

8.12  804 

8.12  808 

9.999% 

50 

10 

8. 21  319 

8. 21  324 

9.99  994 

50 

20 

8. 12  %1 

8.12%i 

9.999% 

40 

20 

8. 21  447 

8.  21 453 

9.99  994 

40 

30 

8. 13  117 

8. 13  121 

9.99  9% 

30 

30 

8. 21  576 

8. 21  581 

9.99994 

30 

40 

8. 13  272 

8. 13  276 

9.999% 

20 

40 

8.  21  703 

8. 21  709 

9.99994 

20 

50 

8. 13  427 

8. 13  431 

9.999% 

10 

50 

8.21831 

8. 21  837 

9.99  994 

10 

470 

8. 13  581 

8. 13  585 

9.99  9% 

013 

67  0 

8.21958 

8.21964 

9.99994 

0    3 

10 

8. 13  735 

8. 13  739 

9.999% 

50 

10 

8.22  08i 

8.22  091 

9.99994 

50 

20 

8.13  888 

8. 13  892 

9.999% 

40 

20 

8.  22  211 

8.  22  217 

9.99994 

40 

30 

8. 14  (HI 

8. 14  (Hi 

9.999% 

30 

30 

8.22  337 

8.  22  343 

9.99994 

30 

40 

8. 14  193 

8. 14  197 

9.99  9% 

20 

40 

8.  22  463 

8.22  469 

9.99994 

20 

50 

8.14  344 

8.14  348 

9.99  9% 

10 

50 

8.  22  588 

8.22  595 

9.99994 

10 

480 

8.14  495 

8. 14  500 

9.999% 

012 

68  0 

8. 22  713 

8. 22  720 

9.99994 

0    2 

10 

8.14  646 

8.14  650 

9.99  9% 

50 

10 

8. 22  838 

8.  22  844 

9.99994 

50 

20 

8. 14  7% 

8.14  800 

9.999% 

40 

20 

8. 22  %2 

8.22%8 

9.99994 

40 

30 

8.14  945 

8.14950 

9.999% 

30 

30 

8.23  086 

8.  23  092 

9.99994 

30 

40 

8.15  094 

8.15  099 

9.99  9% 

20 

40 

8.  23  210 

8. 23  216 

9.99994 

20 

50 

8. 15  243 

8. 15  247 

9.99  9% 

10 

50 

8. 23  333 

8. 23  339 

9.99994 

10 

490 

8. 15  391 

8. 15  395 

9.999% 

Oil 

69  0 

8. 23  456 

8.  23  462 

9.99994 

0    1 

10 

8. 15  538 

8. 15  543 

9.999% 

50 

10 

8.  23  578 

8.  23  585 

9.99994 

50 

20 

8. 15  685 

8. 15  690 

9.999% 

40 

20 

8.  23  700 

8. 23  707 

9.99994 

40 

30 

8. 15  832 

8. 15  836 

9.999% 

30 

30 

8.  23  822 

8. 23  829 

9.99993 

30 

40 

8. 15  978 

8. 15  982 

9.99995 

20 

40 

8.23  944 

8.  23  950 

9.99993 

20 

50 

8. 16 123 

8. 16 128 

9.99995 

10 

50 

8.  24  065 

8.24  071 

9.99993 

10 

5O0 

8.16  268 

8.16  273 

9.99995 

OlO 

6O0 

8.  24  186 

8.  24  192 

9.99993 

0    O 

r  ft 

log  cos 

log  cot 

log  sin 

ff  f 

f  ff 

log  cos 

log  cot 

log  sin 

ff  f 

89' 


1' 


25 


f  ft 

log  sin 

8. 24  186 

log  t4in 

8.  24  192 

log  COS 

ft   t 

t  ft 

log  sin 

log  tan 

log  COS 

9.99  991 

tr  f 

0    0 

9.99993 

06O 

10  0 

8.30879 

8.30  888 

06O 

10 

8.24  306 

8.24  313 

9.99993 

50 

10 

8.30983 

8.30992 

9.99  991 

50 

20 

8. 24  426 

8.24  433 

9.99993 

40 

20 

8.31086 

8. 31 095 

9.99  991 

40 

30 

8. 24  546 

8.  24  553 

9.99993 

30 

30 

8. 31 188 

8. 31 198 

9.99  991 

30 

40 

8.  24  665 

8.  24  672 

9.99993 

20 

40 

8. 31  291 

8. 31  300 

9.99  991 

20 

50 

8.24  785 

8.  24  791 

9.99993 

10 

50 

8.31393 

8.31403 

9.99991 

10 

1    0 

8.24903 

8.24  910 

9.99993 

069 

110 

8.31495 

8. 31  505 

9.99  991 

049 

10 

8. 25  022 

8.  25  029 

9.99993 

50 

10 

8.31597 

8.31606 

9.99991 

50 

20 

8.  25  140 

8.25147 

9.99  993 

40 

20 

8.  31 699 

8. 31  708 

9.99  991 

40 

30 

8.  25  258 

8. 25  265 

9.99  993 

30 

30 

8.  31  800 

8. 31  809 

9.99991 

30 

40 

8. 25  375 

8. 25  382 

9.99993 

20 

40 

8.  31  901 

8.31911 

9.99991 

20 

50 

8. 25  493 

8. 25  500 

9.99993 

10 

50 

8.32  002 

8.32012 

9.99991 

10 

2    0 

8.25  609 

8. 25  616 

9.99993 

068 

12  0 

8.32103 

8.32112 

9.99990 

048 

10 

8. 25  726 

8.  25  733 

9.99  993 

50 

10 

8.  32  203 

8. 32  213 

9.99990 

50 

20 

8.  25  842 

8.25  849 

9.99993 

40 

20 

8.32  303 

8.32  313 

9.99990 

40 

30 

8.  25  958 

8.  25  %5 

9.99  993 

30 

30 

8.32  403 

8.32  413 

9.99  990 

30 

40 

8.26074 

8.26081 

9.99993 

20 

40 

8.  32  503 

8.32  513 

9.99  990 

20 

50 

8.  26 189 

8.  26  196 

9.99  993 

10 

50 

8. 32  602 

8.32  612 

9.99  990 

10 

3    0 

8.26304 

8.26312 

9.99993 

067 

13  0 

8.32  702 

8.  32  711 

9.99990 

047 

10 

8.26  419 

8.26  426 

9.99  993 

50 

10 

8. 32  801 

8.32  811 

9.99990 

50 

20 

8.  26  533 

8.  26  541 

9.99  993 

40 

20 

8.32  899 

8.32  909 

9.99  990 

40 

30 

8.26648 

8.  26  655 

9. 99  993 

30 

30 

8.32  998 

8.33  008 

9.99  990 

30 

40 

8.  26  761 

8.  26  769 

9.99  993 

20 

40 

8.33  0% 

8.  ZZ  106 

9.99990 

20 

50 

8.26  875 

8.26882 

9.99993 

10 

50 

8.33195 

8. 33  205 

9.99990 

10 

4    0 

8.26  988 

8.26996 

9.99  992 

066 

14  0 

8. 33  292 

8. 33  302 

9.99  990 

046 

10 

8. 27  101 

8.  27  109 

9.99992 

50 

10 

8.33  390 

8.33  400 

9.99  990 

50 

20 

8. 27  214 

8.  27  221 

9.99992 

40 

20 

8.  Zi  488 

8. 33  498 

9.99  990 

40 

30 

8.  27  326 

8.  27  334 

9.99  992 

30 

30' 

8. 33  585 

8.  ZZ  595 

9.99  990 

30 

40 

8.27  438 

8.  27  446 

9.99  992 

20 

40 

8.  33  682 

8. 33  692 

9.99990 

20 

50 

8.  27  550 

8.  27  558 

9.99992 

10 

50 

8.33  779 

8.33  789 

9.99990 

10 

6    0 

8.27661 

8.27669 

9.99992 

066 

16  0 

8.33  875 

8.33  886 

9.99990 

046 

10 

8. 27  773 

8. 27  780 

9.99992 

50     • 

10 

8.  ZZ  972 

8.33  982 

9. 99  990 

50 

20 

8. 27  883 

8. 27  891 

9.99992 

40 

20 

8.34068 

8.34078 

9.99990 

40 

30 

8. 27  994 

8.28002 

9.99  992 

30 

30 

8. 34  164 

8. 34  174 

9.99990 

30 

40 

8.  28  104 

8.28112 

9.99992 

20 

40 

8.34  260 

8.34  270 

9.99989 

20 

50 

8.28  215 

8.28223 

9.99992 

10 

50 

8.34  355 

8.34366 

9.99  989 

10 

6    0 

8.28324 

8.28  332 

9.99992 

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16  0 

8.34  450 

8.34461 

9.99989 

044 

10 

8.28434 

8.28442 

9. 99  992 

50 

10 

8. 34  546 

8.34  556 

9.99989 

50 

20 

8. 28  543 

8.28  551 

9.99992 

40 

20 

8.34640 

8.34  651 

9.99989 

40 

30 

8.28652 

8.28660 

9.99992 

30 

30 

8. 34  735 

8.34  746 

9.99  989 

30 

40 

8. 28  761 

8.  28  769 

9.99992 

20 

40 

8.34  830 

8. 34  840 

9.99989 

20 

50 

8.  28  869 

8.28  877 

9.99992 

10 

50 

8.34924 

8.34935 

9.99  989 

10 

7    0 

8.28977 

8.28986 

9.99992 

063 

170 

8.35  018 

8.35  029 

9.99989 

043 

10 

8.29085 

8.2909+ 

9.99  992 

50 

10 

8.35112 

8.35123 

9.99989 

50 

20 

8.  29 193 

8.29  201 

9.99  992 

40 

20 

8.  35  206 

8. 35  217 

9.99989 

40 

30 

8.29300 

8.29309 

9.99992 

30 

30 

8. 35  299 

8. 35  310 

9.99  989 

30 

40 

8.29407 

8.29416 

9. 99  992 

20 

40 

8. 35  392 

8.35  403 

9.99989 

.20 

50 

8.29  514 

8.29  523 

9.99  992 

10 

50 

8.35  485 

8.35  497 

9.99989 

10 

8    0 

8.29621 

8.29629 

9.99992 

062 

18  0 

8.35  578 

8. 35  590 

9.99  989 

042 

10 

8. 29  727 

8.  29  736 

9.99  991 

50 

10 

8.35  671 

8.35  682 

9.99  989 

50 

20 

8.29833 

8.29  842 

9.99991 

40 

20 

8.35  764 

8.35  775 

9.99989 

40 

30 

8.29939 

8.29947 

9.99991 

30 

30 

8. 35  856 

8. 35  867 

9.99  989 

30 

40 

8.30044 

8.30053 

9.99991 

20 

40 

8. 35  948 

8. 35  959 

9.99989 

20 

50 

8. 30 150 

8. 30 158 

9.99991 

10 

50 

8.36040 

8.36051 

9.99989 

10 

9    0 

8.30255 

8.30  263 

9.99  991 

0  61 

19  0 

8.36131 

8.36143 

9.99989 

041 

10 

8.30  359 

8.30368 

9.99  991 

50 

10 

8.  36  223 

8.36  235 

9.99  988 

50 

20 

8.30464 

8.30473 

9.99991 

40 

20 

8.36  314 

8. 36  326 

9.99  988 

40 

30 

8.30  568 

8.30  577 

9.99991 

30 

30 

8.36405 

8.36  417 

9.99988 

30 

40 

8.30672 

8.30681 

9.99991 

20 

40 

8.  36  4% 

8. 36  508 

9.99988 

20 

50 

8.  30  776 

8.  30  785 

9.99  991 

10 

50 

8.  36  587 

8. 36  599 

9.99988 

10 

lOO 

8. 30  879 

8.30888 

9.99991 

06O 

2O0 

8.36678 

8.36689 

9.99988 

04O 

f  ft 

log  COS 

log  cot 

log  sin 

ff   t 

f  ff 

log  COS 

log  cot 

log  sin 

ft  t 

88' 


26 


r 


r 


27 


f  ff 


20  0 

10 
20 
30 
40 
50 

210 
10 
20 
30 
40 
SO 

220 
10 
20 
30 
40- 
50 

230 
10 
20 
30 
40 
50 

240 
10 
20 
30 
40 
50 

250 
10 
20 
30 
40 
50 

260 
10 
20 
30 
40 
50 

270 
10 
20 
30 
40 
50 

280 
10 
20 
30 
40 
50 

290 
10 
20 
30 
40 
50 

300 


log  sin     log  tan      log  cos 


9  ff 


8.36678  8.36689  9.9998S 

8.36  768  8.36  780  9.99988 

8.36  858  8.36  870  9.99988 
8.369^8  8.36960  9.99988 

8.37  038  8.37050  9.99988 
8.37128  8.37140  9.99988 

8.37  217  8.37  229  9.99988 

8.37  306  8.37  318  9.99988 

8.37  395  8.37  408  9.99988 

8.37484  8.37  497  9.99  988 

8.37  573  8.37  585  9.99988 

8.37  662  8.37674  9.99988 

8.37  750  8.37  762  9.99988 
8.37838  8.37  850  9.99988 
8.37926  8.37938  9.99988 

8.38  014  8.38026  9. 99  987 
8.38101  8.38114  9.99987 
8.38189  8.38202  9.99987 

8.38  276  8.38  289  9.99987 

8.38  363  8.38  376  9.99987 

8.38  450  8.38463  9.99987 

8.38  537  8.38  550  9.99  987 

8.38624  8.38  636  9.99987 

8.38  710  8.38  723  9.99  987 

8.387%  8.38809  9.99987 

8.38882  8.38  895  9.99  987 

8.38968  8.38981  9.99987 

8.39054  8.39  067  9.99987 

8.39139  8.39153  9.99  987 

8.39225  8.39  238  9.99  987 

8.39310  8.39  323  9.99987 

8.39395  8.39408  9.99987 

8.39480  8.39493  9.99987 

8.39  565  8.39  578  9.99  987 
8.39649  8.39  663  9.99987 
8.39  734  8.39  747  9.99986 

8.39  818  8.39832  9.99986 

8.39902  8.39  916  9.99986 

8.39986  8.40000  9.999S6 

8.40070  8.40083  9.99986 

8.40153  8.40167  9.99  986 

8.40237  8.40251  9.99986 

8.40320  8.40334  9.99986 

8.40403  8.40417  9.99986 

8.40486  8.40  500  9.99986 

8.40569  8.40  583  9.99986 

8.40651  8.40  665  9.99986 

8.40734  8.40  748  9.99  986 

8.40816  8.40830  9.99986 

8.40898  8.40913  9.99986 

8.40980  8.40995  9.99986 

8.41062  8.41077  9.99  986 

8.41144  8.41158  9.99  986 

8.41225  8.41240  9.99986 

8.41307  8.41321  9.99985 

8.41388  8.41403  9.99  985 

8.41469  8.41484  9.99985 

8.41550  8.41565  9.99  985 

8.41631  8.41646  9.99985 

8.41711  8.41726  9.99985 

8.41792  8.41807  9.99985 


ff     9 


log  cos     log  cot      log  sin 


04O 

50 

40 

30 

20 

10 

039 

50 

40 

30 

20 

10 

038 

50 

40 

30 

20 

10 

037 

50 

40 

30 

20 

10 

036 

50 

40 

30 

20 

10 

035 

50 

40 

30 

20 

10 

034 

50 

40 

30 

20 

10 

033 

50 

40 

30 

20 

10 

032 

50 

40 

30 

20 

10 

031 

50 
40 
30 
20 
10 

03O 


'  ' '    log  sin     log  tan     log  cos 


f/   f 


300 

10 
20 
30 
40 
50 

310 
10 
20 
30 
40 
50 

32  0 
10 
20 
30 
40 
50 

330 

10 
20 
30 
40 
50 

340 
10 
20 
30 
40 
50 

350 
10 
20 
30 
40 
50 

360 

10 
20 
30 
40 
50 

37  0 
10 
20 
30 
40 
50 

380 
10 
20 
30 
40 
50 

390 

10 
20 
30 
40 
50 

400 


r  99 


8.41792  8.41807  9. 99  985 

8.41872  8.41887  9.99  985 

8.41952  8.41%7  9.99985 

8.42  032  8.42  018  9.99  985 

8.42112  8.42127  9.99985 

8.42192  8.42  207  9.99985 

8.42  272  8.42  287  9.99985 

8.42  351  8.42366  9.99985 

8.42  430  8.42  446  9.99985 

8.42  510  8.42  525  9.99985 

8.42  589  8.42  60+  9.99985 

8.42  667  8.42683  9.99985 

8.42  746  8.42  762  9.99984 

8.42  825  8.42  840  9.99984 

8.42  903  8.42  919  9.99984 

8.42  982  8.42  997  9.99984 

8.43  060  8.43  075  9.99984 
8.43138  8.43154  9.99984 

8.43  216  8.43  232  9.99984 

8.43  293  8.43  309  9.99984 

8.43  371  8.43  387  9.99984 

8.43  448  8.43  464  9.99984 

8.43  526  8.43  542  9.99984 

8.43  603  8.43  619  9.99984 

8.43680  8.436%  9.99984 

8.43  757  8.43  773  9.99984 

8.43  834  8.43  850  9.99984 

8.43  910  8.43  927  9.99984 

8.43  987  8.44  003  9.99984 
8.44063  8.44080  9.99983 

8.44139  8.44156  9.99983 

8.44  216  8.44  232  9.99  983 
8.44  292  8.44  308  9.99983 
8.44367  8.44384  9.99983 
8.44443  8.44460  9.99983 
8.44  519  8.44  536  9.99983 

8.44594  8.44611  9.99983 

8.44669  8.44686  9.99983 

8.44745  8.44  762  9.99983 

8.44  820  8.44  837  9.99983 
8.44895  8.44912  9.99983 
8.44%9  8.44987  9.99983 

8.45  044  8.45  061  9.99983 
8.45  119  8.45136  9.99983 
8.45193  8.45  210  9.99983 
8.45  267  8.45  285  9.99983 
8.45  341  8.45  359  9.99982 
8.45  415  8.45  433  9.99982 

8.45  489  8.45  507  9.99982 

8.45  563  8.45  581  9.99982 

8.45  637  8.45  655  9.99982 

8.45  710  8.45  728  9.99982 

8.45  784  8.45  802  9.99982 

8.45  857  8.45  875  9.99982 

8.45  930  8.45  948  9.99982 
8.46003  8.46021  9.99982 
8.46076  8.46094  9.99982 
8.46149  8.46167  9.99982 

8.46  222  8.46  240  9.99982 
8.46294  8.46  312  9.99  982 

8.46  366  8.46385  9.99982 


99  f 


log  cos      log  cot     log  sin 


03O 

50 
40 
30 
20 
10 

029 

50 
40 
30 
20 
10 

0  28 

50 

40 

30 

20 

10 

027 

50 

40 

30 

20 

10 

0  26 

50 

40 

30 

20 

10 

0  25 

50 

40 

30 

20 

10 

024 

50 

40 

30 

20 

10 

0  23 

50 

40 

30 

20 

10 

0  22 

50 

40 

30 

20 

10 

0  21 

50 

40 

30 

20 

10 

020 


99   9 


88' 


f    99 

log  sin 

8.46366 

log  tan 

8.46385 

log  COS 

99   9 

9    99 

log  sin 

8.50  504 

log  tan 

log  cos 

9.99978 

99  9 

400 

9.99982 

020 

500 

8.50  527 

010 

10 

8.46439 

8. 46  457 

9.99982 

50 

10 

8.50  570 

8.50  593 

9.99978 

50 

20 

8.46  511 

8.'46  529 

9.99982 

40 

20 

8.50  636 

8.50658 

9.99  978 

40 

30 

8. 46  583 

8.46  602 

9.99981 

30 

30 

8.  50  701 

8.  50  724 

9.99  978 

30 

40 

8.46  655 

8.  46  674 

9.99981 

20 

40 

8. 50  767 

8.  50  789 

9.99977 

20 

50 

8.46  727 

8. 46  745 

9.99981 

10 

50 

8.50832 

8.50  855 

9.99977 

10 

410 

8.46  799 

8.46817 

9.99981 

019 

510 

8.50  897 

8.50920 

9.99977 

0    9 

10 

8.46  870 

8.46889 

9.99981 

50 

10 

8.50%3 

8.50985 

9.99977 

50 

20 

8.46942 

8.46960 

9.99981 

40 

20 

8.51028 

8.  51 050 

9.99977 

40 

30 

8.47  013 

8.47  032 

9.99981 

30 

30 

8.51092 

8.51115 

9.99977 

30 

40 

8.47  084 

8. 47  103 

9.99981 

20 

40 

8.  51 157 

8.51180 

9.99977 

20 

50 

8. 47  155 

8.47174 

9.99  981 

10 

50 

8.  51  222 

8.  51  245 

9.99977 

10 

420 

8. 47  226 

8.47  245 

9.99981 

018 

52  0 

8.  51  287 

8. 51  310 

9.99977 

0    8 

10 

8. 47  297 

8. 47  316 

9.99981 

50 

10 

8.  51  351 

8.  51  374 

9.99977 

50 

20 

8.47  368 

8.47  387 

9.99981 

40 

20 

8.  51  416 

8.51439 

9.99977 

40 

30 

8.47  439 

8. 47  458 

9.99981 

30 

30 

8.  51 480 

8. 51  503 

9.99  977 

30 

40 

8. 47  509 

8. 47  528 

9.99981 

20 

40 

8.  51  544 

8.  51  568 

9.99977 

20 

50 

8. 47  580 

8. 47  599 

9.99  981 

10 

50 

8.51609 

8. 51 632 

9.99977 

10 

430 

8.47  650 

8.47669 

9.99981 

017 

530 

8.  51  673 

8.  51 6% 

9.99977 

0    7 

10 

8. 47  720 

8. 47  740 

9.99980 

50 

10 

8.  51  737 

8.51760 

9.99976 

50 

20 

8.47  790 

8.47  810 

9.99980 

40 

20 

8.  51  801 

8.  51  824 

9.99976 

40 

30 

8. 47  860 

8.47  880 

9.99  980 

30 

30 

8.  51  864 

8.51888 

9.99976 

30 

40 

8.47  930 

8.47950 

9.99980 

20 

40 

8.  51  928 

8.  51  952 

9.  99  976 

20 

50 

8.48000 

8. 48  020 

9.99  980 

10 

50 

8.  51 992 

8.  52  015 

9.99976 

10 

440 

8.48069 

8.48090 

9.99980 

016 

540 

8.52  055 

8.52  079 

9.99976 

0    6 

10 

8. 48  139 

8. 48  159 

9.99980 

50 

10 

8. 52  119 

8.  52  143 

9.99  976 

50 

20 

8.48  208 

8. 48  228 

9.99980 

40 

20 

8. 52  182 

8.  52  206 

9.99976 

40 

30 

8. 48  278 

8. 48  298 

9.99980 

30 

30 

8.  52  245 

8.  52  269 

9.99976 

30 

40 

8.48  347 

8. 48  367 

9. 99  980 

20 

40 

8.52  308 

8.52  332 

9.99976 

20 

50 

8.48416 

8.48436 

9.99980 

10 

50 

8.52  371 

8. 52  3% 

9.99976 

10 

450 

8.48485 

8.48  505 

9.99980 

015 

55  0 

8.52  434 

8.  52  459 

9.99976 

0    5 

10 

8.48  554 

8. 48  574 

9.99980 

50 

10 

8.52  497 

8. 52  522 

9.99976 

50 

20 

8.48  622 

8. 48  643 

9.99  980 

40 

20 

8.  52  560 

8.52  584 

9.99  976 

40 

30 

8.48691 

8.48  711 

9.99  980 

30 

30 

8.52  623 

8.52  647 

9.99975 

30 

40 

8. 48  760 

8. 48  780 

9.99979 

20 

40 

8.52  685 

8.52  710 

9.99975 

20 

50 

8.48828 

8.48  849 

9.99979 

10 

50 

8. 52  748 

8. 52  772 

9.99  975 

10 

460 

8.48896 

8.48917 

9.99979 

014 

56  0 

8.52  810 

8. 52  835 

9.99975 

0    4 

10 

8.48  965 

8.48985 

9.99979 

50 

10 

8. 52  872 

8.  52  897 

9.99975 

50 

20 

8.49  033 

8.49053 

9.99979 

40 

20 

8.52  935 

8.52960 

9.99975 

40 

30 

8.49101 

8. 49 121 

9.99979 

30 

30 

8.52  997 

8.  53  022 

9.99975 

30 

40 

8. 49  169 

8. 49 189 

9.99979 

20 

40 

8.53  059 

8.  53  084 

9.99975 

20 

50 

8.49  236 

8.49  257 

9.99979 

10 

50 

8. 53  121 

8. 53  146 

9.99975 

10 

470 

8.49304 

8.49325 

9.99979 

013 

57  0 

8.  53  183 

8. 53  208 

9.99975 

0    3 

10 

8.49372 

8.49  393 

9.99979 

50 

10 

8.  53  245 

8. 53  270 

9.99975 

50 

20 

8.49439 

8. 49  460 

9.99979 

40 

20 

8.  53  306 

8. 53  332 

9.99975 

40 

30 

8.49  506 

8.49  528 

9.99979 

30 

30 

8. 53  368 

8.  53  393 

9.99975 

30 

40 

8. 49  574 

8.49  595 

9.99979 

20 

40 

8.  53  429 

8.  SZ  455 

9.99975 

20 

50 

8.49641 

8.49662 

9.99979 

10 

50 

8. 53  491 

8.53  516 

9.99974 

10 

480 

8. 49  708 

8. 49  729 

9.99979 

012 

58  0 

8.53  552 

8. 53  578 

9.99974 

0    2 

10 

8.49775 

8. 49  796 

9.99979 

50 

10 

8. 53  614 

8.  53  639 

9.99974 

50 

20 

8.49  842 

8.49863 

9.99978 

40 

20 

8. 53  675 

8.  53  700 

9.99974 

40 

30 

8.49908 

8.49930 

9.99978 

30 

30 

8.53  736 

8.  53  762 

9.99974 

30 

40 

8.49  975 

8.49997 

9.99978 

20 

40 

8. 53  797 

8. 53  823 

9.99974 

20 

50 

8.50042 

8.50063 

9.99978 

10 

50 

8.53  858 

8. 53  884 

9.99974 

10 

490 

8.  50 108 

8. 50 130 

9.99978 

Oil 

59  0 

8.53  919 

8.53945 

9.99974 

0    1 

10 

8.  50  174 

8. 50 196 

9.99978 

50 

10 

8.  53  979 

8.54005 

9.99974 

50 

20 

8.50  241 

8. 50  263 

9.99978 

40 

20 

8.54040 

8.54066 

9.99974 

40 

30 

8.50307 

8.50329 

9.99978 

30 

30 

8. 54 101 

8.54127 

9.99  974 

30 

40 

8.50  373 

8.50395 

9.99  978 

20 

40 

8.  54 161 

8.  54  187 

9.99974 

20 

50 

8.50439 

8.50461 

9.99978 

10 

50 

8. 54  222 

8. 54  248 

9.99974 

10 

500 

8.50504 

8.50  527 

9.99978 

010 

6O0 

8.54  282 

8.54308 

9.99974 

0  0 

9  99 

log  cos 

log  cot 

log  sin 

99    9 

9    9t 

log  COS 

log  cot 

log  sin 

99  t 

88' 


f 


I\ 


ill 


i  : 


i:  r 


28 

r 

/ 

log  sin 

log  tan 

log  cot 

log  008 

f 

8 

24186 

8 

24192 

11 

75  808 

9 

99993 

o 

60 

1 

24  903 

24910 

75  090 

99993 

59 

2 

25  609 

25  616 

74  384 

99993 

58 

3 

26304 

26312 

73  688 

99993 

57 

4 

26988 

26996 

73  00+ 

99992 

56 

5 

27661 

27  669 

72  331 

99992 

55 

6 

28324 

28  332 

71668 

99992 

54 

7 

28977 

28986 

71014 

99992 

53 

8 

29621 

29629 

70371 

99992 

52 

9 

3025i 

30  263 

69  737 

99991 

51 

lO 

30879 

30  888 

69112 

99991 

50 

11 

31 495 

31505 

68495 

99991 

49 

12 

32103 

32112 

67  888 

99990 

48 

13 

32  702 

32  711 

67  289 

99  990 

47 

14 

33  292 

33  302 

66698 

99990 

46 

15 

33  875 

33  886 

66114 

99990 

45 

16 

34  450 

34  461 

65  539 

99989 

44 

17 

35  018 

35  029 

64971 

99  989 

43 

IS 

35  578 

35  590 

6+410 

99  989 

42 

19 

36131 

36143 

63  857 

99989 

41 

20 

36678 

36689 

63  311 

99988 

40 

21 

37  217 

37  229 

62  771 

99  988 

39 

22 

37  750 

37  762 

62  238 

99988 

38 

23 

38  276 

38  289 

61711 

99987 

37 

24 

38  796 

38  809 

61191 

99987 

36 

25 

39  310 

39  323 

60  677 

99987 

35 

26 

39  818 

39  832 

60168 

99986 

34 

27 

40  320 

40334 

59666 

99986 

33 

28 

40  816 

40830 

59170 

99  986 

32 

29 

41307 

41321 

58  679 

99985 

31 

30 

41792 

41807 

58193 

99985 

30 

31 

42  272 

42  287 

57  713 

99985 

29 

32 

42  746 

42  762 

57  238 

99984 

28 

33 

43  216 

43  232 

56  768 

99  984 

27 

34 

43  680 

43  696 

56304 

99984 

26 

35 

44139 

44156 

55  844 

99983 

25 

36 

44  594 

44611 

55  389 

99983 

24 

37 

45  OH 

45  061 

54  939 

99  983 

23 

38 

45  489 

45  507 

54493 

99982 

22 

39 

45  930 

45  9^8 

54052 

99982 

21 

40 

46366 

46385 

53  615 

99982 

20 

41 

46  799 

46  817 

53  183 

99981 

19 

42 

47  226 

47  245 

52  755 

99  981 

18 

43 

47  650 

47  669 

52  331 

99981 

17 

44 

48069 

48089 

51911 

99980 

16 

45 

48  485 

48  505 

51495 

99980 

15 

46 

48  8% 

48917 

51083 

99979 

14 

47 

49  304 

49  325 

50  675 

99  979 

13 

48 

49  708 

49  729 

50  271 

99979 

12 

49 

50108 

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O 

9 

log  008 

9 

log  cot 

lO 

log  tan 

9 

log  sin 

r 

f 

83^ 


T 


8° 


81 


o 


8 


lO 

11 
12 
13 
14 

15 

16 
17 
18 
19 

20 

21 
22 
23 
24 

25 

26 
27 
28 
29 

30 

31 
32 
33 
34 

35 

36 
37 
38 
39 

40 

41 
42 
43 
44 

45 

46 
47 
48 
49 

50 

51 
52 
53 
54 

55 

56 

57 
58 
59 

60 


log  sin     log  tan    log  cot     log  cos 


9 


lO 


9 


08  589  08914  91086  99675 

08692  09019  90981  99674 

08  795  09123  90  877  99672 

08  897  09  227  90  773  99  670 
08999  09330  90670  99669 

09101  09434  90  566  99667 

09202  09537  90463  99666 

09304  09640  90360  99664 

09  405  09  742  90  258  99663 
09  506  09  845  90155  99661 

09606  09947  90053  99659 

09  707  100+9  89951  99658 

09  807  10150  89  850  99  656 

09  907  10252  89  748  99655 
10006  10353  89647  99653 

10106  10454  89  546  99651 

10  205  10  555  89445  99  650 
10  30+  10656  893+4  99648 
10402  10  756  89  244  99  647 
10  501  10856  89144  99645 

10  599  10956  89044  99643 

10697  11056  88  944  99642 

10  795  11155  88  845  99640 

10893  11254  88  746  99638 

10990  11353  88647  99637 

11087  11452  88  548  99635 

11184  11551  88449  99633 

11281  11649  88351  99632 

11377  11747  88  253  99630 

11474  11845  88155  99629 

11570  119+3  88  057  99627 

11666  12  0+0  87  960  99625 

11761  12138  87  862  99624 

11857  12  235  87  765  99622 

11952  12  332  87  668  99620 

120+7  12  428  87  572  99618 

12142  12  525  87  475  99617 

12  236  12  621  87  379  99615 

12  331  12  717  87  283  99613 

12  425  12  813  87187  99612 

12  519  12  909  87  091  99610 

12612  13004  869%  99608 

12  706  13  099  86901  99607 

12  799  13194  86806  99605 

12  892  13  289  86  711  99  603 

12  985  13  384  86616  99  601 

13  078  13  478  86  522  99  600 
13171  13  573  86427  99  598 
13  263  13  667  86333  99  5% 
13  355  13  761  86239  99  595 

13  447  13  854  86146  99  593 

13  539  13  948  86052  99  591 

13  630  14  041  85  959  99  589 

13  722  14134  85  866  99  588 

13  813  14  227  85  773  99  586 

13  904  14320  85  680  99  584 

13  994  14  412  85  588  99  582 
14085  14  504  85  4%  99  581 
14175  14  597  85  403  99  579 

14  266  14  688  85  312  99  577 

14  356  14  780  85  220  99  575 


9 


9 


lO 


9 


log  008    logoot    log  tan    log  sin 

8? 


60 

59 
58 
57 
56 

55 

54 
53 

52 
51 

50 

49 
48 
47 
46 

45 

44 
43 
42 
41 

40 

39 
38 
37 
36 

35 

34 
2^^ 
32 
31 

30 

29 
28 
27 
26 

25 

24 
23 
22 
21 

20 

19 
18 
17 
16 

15 

14 
13 
12 
11 

10 

9 

8 


O 


O 


8 


lO 

11 

12 
13 
14 

15 

16 
17 
18 
19 

20 

21 
22 
23 
24 

25 

26 

27 
28 
29 

30 

31 
32 
33 
34 

35 

36 
37 
38 
39 

40 

41 
42 
43 
44 

45 

46 
47 
48 
49 

50 

51 
52 
53 
54 

55 

56 
57 
58 
59 

60 


log  sin    log  tan    log  cot    log  cos 


9 


9 


lO 


9 


14  356  14  780  85  220  99  575 

14  445  14  872  85  128  99  574 

14  535  14  %3  85  037  99  572 

14  624  15  054  84  946  99  570 

14  714  15145  84  855  99  568 

14  803  15  236  84  764  99  566 
14891  15  327  84  673  99  565 
14980  15  417  84  583  99  563 

15  069  15  508  84  492  99  561 
15157  15  598  84  402  99  559 
15  245  15  688  84  312  99  557 
15  333  15  777  84  223  99  556 
15  421  15  867  84133  99  554 
15  508  15  956  84  044  99  552 
15  5%  16  046  83  954  99550 

15  683  16135  83  865  99  5+8 

15  770  16224  83  776  99  5+6 

15  857  16312  83  688  99  545 

15  944  16  401  83  599  99  5+3 
16030  16489  83  511  99  541 

16116  16  577  83  423  99  539 

16  203  16  665  83  335  99  537 
16  289  16  753  83  2+7  99  535 
16374  16  841  83159  99  533 
16460  16928  83072  99532 

16  545  17  016  82  984  99  530 

16  631  17103  82  897  99  528 

16  716  17190  82  810  99  526 

16  801  17  277  82  723  99  524 

16886  17  363  82  637  99522 

16  970  17450  82  550  99  520 

17  055  17  536  82  464  99  518 
17139  17  622  82  378  99  517 
17  223  17  708  82  292  99  515 
17  307  17  794  82  206  99513 

17  391  17  880  82120  99511 

17  474  17  %5  82035  99  509 

17  558  18051  81949  99  507 

17  641  18136  81864  99  505 

17  724  18  221  81779  99  503 

17807  18  306  81694  99  501 

17  890  18  391  81609  99499 
17973  18475  81525  99497 
18055  18  560  81440  99495 
18137  18  6+4  81356  99  494 

18  220  18  728  81272  99  492 
18  302  18  812  81188  99490 
18383  188%  81104  99488 
18465  18979  81021  99486 
18  547  19063  80937  99484 

18628  19146  80854  99  482 

18  709  19  229  80  771  99480 

18  790  19312  80688  99  478 

18871  19395  80605  99476 

18952  19478  80  522  99474 

19033  19  561  80439  99472 

19113  19643  80357  99470 

19193  19  725  80275  99  468 

19273  19807  80193  99466 

19353  19889  80111  99464 

19433  19  971  80029  99462 


9 


9 


lO 


9 


log  cos    log  cot    logtaa    log  sin 

8? 


60 

59 
58 
57 
56 

55 

54 
53 
52 
51 

50 

49 
48 
47 
46 

45 

44 
43 
42 
41 

40 

39 
38 
37 
36 

35 

34 
33 
32 
31 

30 

29 
28 
27 
26 

25 

24 
23 
22 
21 

20 

19 
18 
17 
16 

15 

14 
13 
12 
11 

lO 

9 
8 


O 


y 


32 


m 


ir 


12° 


83 


M 


f 

log  sin 

log  tan 

log  oot 

log  008 

f 

f 

log  sin 

log  tan 

log  cot 

log  COS 

f 

9 

19433 

9 

19971 

lO 

80029 

9 

99  462 

9 

23  %7 

9 

24  632 

lO 

75  368 

9 

99  335 

o 

60 

o 

60 

1 

19513 

20053 

79947 

99  460 

59 

1 

24  039 

24  706 

75  294 

99  333 

59 

2 

19592 

20134 

79  866 

99  458 

58 

2 

24110 

24  779 

75  221 

99331 

58 

3 

19672 

20  216 

79  784 

99  456 

57 

3 

24181 

24  853 

75  147 

99  328 

57 

4 

19  751 

20  297 

79  703 

99454 

56 

4 

24  253 

24  926 

75  074 

99  326 

56 

5 

19  830 

20378 

79622 

99452 

55 

5 

24  324 

25  000 

75  000 

99324 

55 

6 

19909 

20459 

79541 

99450 

54 

6 

24  395 

25  073 

74  927 

99  322 

54 

7 

19988 

20  540 

79460 

99448 

53 

7 

24  466 

25146 

74  854 

99  319 

53 

8 

20067 

20621 

79  379 

99446 

52 

8 

24  536 

25  219 

74  781 

99317 

52 

9 

20145 

20  701 

79  299 

99  444 

51 

9 

24  607 

25  292 

74  708 

99315 

51 

lO 

20  223 

20  782 

79  218 

99442 

50 

lO 

24  677 

25  365 

74  635 

99  313 

50 

11 

20302 

20862 

79138 

99440 

49 

11 

24  748 

25  437 

74  563 

99310 

49 

12 

20380 

209+2 

79058 

99438 

48 

12 

24  818 

25  510 

74  490 

99  308 

48 

13 

20  458 

21022 

78  978 

99436 

47 

13 

24  888 

25  582 

74  418 

99  306 

47 

14 

20535 

21102 

78898 

99434 

46 

14 

24958 

25  655 

74  345 

99304 

46 

16 

20613 

21182 

78818 

99432 

45 

15 

25  028 

25  727 

74  273 

99301 

45 

16 

20691 

21261 

78  739 

99429 

44 

16 

25  098 

25  799 

74  201 

99  299 

44 

17 

20  768 

21341 

78659 

99427 

43 

17 

25  168 

25  871 

74  129 

99  297 

43 

18 

20845 

21420 

78  580 

99425 

42 

18 

25  237 

25  943 

74  057 

99  294 

42 

19 

20922 

21499 

78  501 

99423 

41 

19 

25  307 

26015 

73  985 

99292 

41 

20 

20999 

21578 

78422 

99421 

40 

20 

25  376 

26086 

73  914 

99290 

40 

21 

21076 

21657 

78  343 

99  419 

39 

21 

25  445 

26158 

73  842 

99  288 

39 

22 

21153 

21736 

78  264 

99417 

38 

22 

25  514 

26229 

73  771 

99  285 

38 

23 

21229 

21814 

78186 

99415 

37 

23 

25  583 

26301 

73  699 

99  283 

37 

24 

21306 

21893 

78107 

99  413 

36 

24 

25  652 

26372 

73  628 

99  281 

36 

25 

21382 

21971 

78029 

99411 

35 

25 

25  721 

26  443 

73  557 

99  278 

35 

26 

21458 

22  019 

77951 

99409 

34 

26 

25  790 

26  514 

73  486 

99  276 

34 

27 

21534 

22127 

77  873 

99  407 

33 

27 

25  858 

26  585 

73  415 

99  274 

33 

28 

21610 

22  205 

77  795 

99404 

32 

28 

25  927 

26655 

73  345 

99  271 

32 

29 

21685 

22  283 

77  717 

99402 

31 

29 

25  995 

26  726 

73  274 

99  269 

31 

30 

21761 

22  361 

77639 

99  400 

30 

30 

26063 

26  797 

73  203 

99  267 

30 

31 

21836 

22  438 

77  562 

99  398 

29 

31 

26131 

26  867 

73133 

99  264 

29 

32 

21912 

22  516 

77  484 

99  3% 

28 

32 

26199 

26937 

73  063 

99  262 

28 

33 

21987 

22  593 

77  407 

99  394 

27 

33 

26  267 

27  008 

72  992 

99  260 

27 

34 

22  062 

22  670 

77  330 

99  392 

26 

34 

26335 

27  078 

72  922 

99  257 

26 

35 

22137 

22  747 

77  253 

99390 

25 

35 

26403 

27148 

72  852 

99  255 

25 

36 

22  211 

22  824 

77176 

99  388 

24 

36 

26470 

27  218 

72  782 

99  252 

24 

37 

22  286 

22  901 

77099 

99  385 

23 

37 

26  538 

27  288 

72  712 

99  250 

23 

38 

22  361 

22  977 

77023 

99  383 

22 

38 

26  605 

27  357 

72  643 

99  248 

22 

39 

22  435 

23  054 

76946 

99  381 

21 

39 

26672 

27  427 

72  573 

99  245 

21 

40 

22  509 

23130 

76  870 

99379 

20 

40 

26  739 

27  4% 

72  504 

99  243 

20 

41 

22  583 

23  206 

76  794 

99  377 

19 

41 

26806 

27  566 

72  434 

99  241 

19 

42 

22  657 

23  283 

76  717 

99375 

18 

42 

26  873 

27  635 

72  365 

99  238 

18 

43 

22  731 

23  359 

76641 

99372 

17 

43 

26940 

27  704 

72  2% 

99  236 

17 

44 

22  805 

23  435 

76  565 

99370 

16 

44 

27  007 

27  773 

72  227 

99  233 

16 

45 

22  878 

23  510 

76490 

99368 

15 

45 

27073 

27  842 

72158 

99  231 

15 

46 

22  952 

23  586 

76414 

99  366 

14 

46 

27140 

27  911 

72  089 

99  229 

14 

47 

23  025 

23  661 

76339 

99  364 

13 

47 

27  206 

27980 

72  020 

99  226 

13 

48 

23  098 

23  737 

76  263 

99  362 

12 

48 

27  273 

280+9 

71951 

99224 

12 

49 

23171 

23  812 

76188 

99359 

11 

49 

27  339 

28117 

71883 

99  221 

11 

50 

23  244 

23  887 

76113 

99  357 

10 

50 

27  405 

28186 

71814 

99  219 

lO 

51 

23  317 

23  962 

76038 

99  355 

9 

51 

27  471 

28  254 

71746 

99  217 

9 

52 

23  390 

24037 

75  963 

99353 

8 

52 

27  537 

28323 

71677 

99  214 

8 

53 

23  462 

24112 

75  888 

99351 

7 

53 

27  602 

28391 

71609 

99  212 

7 

54 

23  535 

24186 

75  814 

99348 

6 

54 

27  668 

28459 

71541 

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6 

55 

23  607 

24  261 

75  739 

99  346 

5 

55 

27  734 

28  527 

71473 

99  207 

5 

56 

23  679 

24  335 

75  665 

99  344 

4 

56 

27  799 

28  595 

71405 

99  204 

4 

57 

23  752 

24410 

75  590 

99  342 

3 

57 

27  864 

28662 

71338 

99  202 

3 

58 

23  823 

24  484 

75  516 

99340 

2 

58 

27  930 

28  730 

71270 

99  200 

2 

59 

23  895 

24  558 

75  442 

99  337 

1 

59 

27  995 

28  798 

71202 

99197 

1 

60 

23  %7 

24  632 

75  368 

99  335 

O 

60 

28  060 

28865 

71135 

99195 

O 

9 

log  008 

9 

log  cot 

lO 

log  tan 

9 

log  sin 

9 

log  008 

9 

log  cot 

lO 

log  tan 

9 

log  sin 

f 

f 

f 

f 

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log  sin 

log  tan 

log  cot 

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9 

28060 

9 

28  865 

10 

71135 

9 

99195 

9 

31788 

9 

32  747 

lO 

67  253 

9 

99040 

0 

60 

o 

60 

1 

28125 

28933 

71067 

99192 

59 

1 

31847 

32  810 

67190 

99038 

59 

2 

28190 

29  000 

71000 

99190 

58 

2 

31907 

32  872 

67128 

99035 

58 

3 

28  254 

29  067 

70933 

99187 

57 

3 

31966 

32  933 

67  067 

99032 

57 

4 

28  319 

29134 

70866 

99185 

56 

4 

32  025 

32  995 

67  005 

99030 

56 

5 

28  384 

29  201 

70  799 

99182 

56 

5 

32  084 

33  057 

66943 

99027 

66 

6 

28448 

29  268 

70  732 

99180 

54 

6 

32143 

33119 

66881 

99024 

54 

7 

28  512 

29  335 

70665 

99177 

53 

7 

32  202 

33180 

66820 

99022 

53 

8 

28  577 

29  402 

70  598 

99175 

52 

8 

32  261 

33  242 

66  758 

99019 

52 

9 

28641 

29468 

70  532 

99172 

51 

9 

32  319 

33  303 

66697 

99016 

51 

10 

28  705 

29  535 

70465 

99170 

50 

lO 

32  378 

33  365 

66635 

99013 

50 

11 

28  769 

29  601 

70399 

99167 

49 

11 

32  437 

33  426 

66  574 

99  011 

49 

12 

28833 

29668 

70332 

99165 

48 

12 

32  495 

33  487 

66513 

99008 

48 

13 

28  8% 

29  734 

70  266 

99162 

47 

13 

32  553 

33  548 

66452 

99005 

47 

14 

28960 

29  800 

70  200 

99160 

46 

14 

32  612 

33  609 

66391 

99002 

46 

15 

29024 

29866 

70134 

99157 

45 

15 

32  670 

33  670 

66330 

99000 

45 

16 

29087 

29932 

70068 

99155 

44 

16 

32  728 

33  731 

66  269 

98  997 

44 

17 

29150 

29998 

70002 

99152 

43 

17 

32  786 

33  792 

66  208 

98  994 

43 

18 

29  214 

30064 

69  936 

99150 

42 

18 

32  844 

33  853 

66147 

98  991 

42 

19 

29  277 

30130 

69  870 

99147 

41 

19 

32  902 

33  913 

66087 

98989 

4L 

20 

29340 

30195 

69805 

99145 

40 

20 

32  960 

33974 

66026 

98986 

40 

21 

29  403 

30  261 

69  739 

99142 

39 

21 

33  018 

34  034 

65  966 

98  983 

39 

22 

29466 

30326 

69  674 

99140 

38 

22 

33  075 

34  095 

65  905 

98980 

38 

23 

29  529 

30391 

69609 

99137 

37 

23 

33133 

34155 

65  845 

98978 

37 

24 

29  591 

30457 

69  543 

99135 

36 

24 

33190 

34  215 

65  785 

98975 

36 

25 

29654 

30522 

69478 

99132 

35 

25 

33  248 

34  276 

65  724 

98972 

35 

26 

29  716 

30587 

69413 

99130 

34 

26 

33  305 

34336 

65  664 

98969 

34 

27 

29  779 

30652 

69  348 

99127 

33 

27 

33  362 

34  3% 

65  604 

98967 

33 

28 

29  841 

30  717 

69  283 

99124 

32 

28 

33  420 

34  456 

65  544 

98  %4 

32 

29 

29  903 

30  782 

69  218 

99122 

31 

29 

33  477 

34  516 

65  484 

98  %1 

31 

30 

29966 

30846 

69154 

99119 

30 

30 

33  534 

34  576 

65  424 

98958 

30 

31 

30028 

30911 

69  089 

99117 

29 

31 

33  591 

34  635 

65  365 

98955 

29 

32 

30090 

30975 

69025 

99114 

28 

32 

33  647 

34  695 

65  305 

98953 

28 

33 

30151 

^1040 

68  960 

99112 

27 

33 

33  704 

34  755 

65  245 

98950 

27 

34 

30213 

31104 

688% 

99109 

26 

34 

33  761 

34  814 

65  186 

98947 

26 

35 

30275 

31168 

68  832 

99106 

25 

35 

33  818 

34874 

65126 

98944 

26 

36 

30336 

31233 

68  767 

99104 

24 

36 

33  874 

34  933 

65  067 

98941 

24 

37 

30398 

31297 

68  703 

99101 

23 

37 

33  931 

34  992 

65  008 

98938 

23 

38 

30459 

31361 

68639 

99099 

22 

38 

33  987 

35  051 

64  949 

98936 

22 

39 

30  521 

31425 

68  575 

990% 

21 

39 

34  043 

35111 

64  889 

98  933 

21 

40 

30  582 

31489 

68  511 

99093 

20 

40 

34100 

35  170 

64  830 

98930 

20 

41 

30643 

31552 

68  448 

99091 

19 

41 

34  156 

35  229 

64  771 

98  927 

19 

42 

30  704 

31616 

68  384 

99088 

18 

42 

34  212 

35  288 

64  712 

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60 

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57  358 
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38  206 
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63  031 
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63  205 
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63  275 

63  310 
63  345 
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63  484 
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63  830 
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64  072 
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36  516 
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16 
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21 
22 
23 
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25 

26 

27 
28 
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31 
32 
33 
34 

35 

36 
37 
38 
39 

40 

41 
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44 

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46 
47 
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52 
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55 

56 

57 
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log  sin 

9 

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62  021 

62  049 
62  076 
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62  214 
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62  268 
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62  323 
62  350 
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65  366 
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65  535 
65  568 
65  602 
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703 


65 
65  736 
65  770 
65  803 
65  837 

65  870 
65  904 
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65  971 
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66104 
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66  204 
66  238 
66  271 
66  304 
66  337 

66  371 
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66  437 
66  470 
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66  537 
66  570 
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35  142 
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35  074 
35  040 
35  006 

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34  904 
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34  836 

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34  769 
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34  667 

34634 
34  600 
34  566 
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34  465 
34  432 
34  398 
34  364 
34  331 

34  297 
34  264 
34  230 
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34  096 
34  063 
34  029 
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33  %2 
33  929 
33  8% 
33  862 
33  829 

33  796 
33  762 
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33  696 
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33  629 
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33  430 
33  397 
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33  298 
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95  948 
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95  931 
95  925 
95  920 
95  914 
95  908 

95  902 
95  897 
95  891 
95  885 
95  879 

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58 
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60 


log  tin 

9 

81694 
81709 
81723 
81738 
81752 

81767 
81781 
817% 
81810 
81825 

81839 
81854 
81868 
81882 
81897 

81911 
81926 
81940 
81955 
81969 

81983 
81998 
82  012 
82026 
82  041 

82  055 
82069 
82  084 
82098 
82112 

82126 
82141 
82155 
82169 
82184 

82198 
82  212 
82  226 
82  240 
82  255 

82  269 
82  283 
82  297 
82311 
82326 

82  340 
82354 
82  368 
82382 
823% 

82410 
82424 
82  439 
82  453 
82467 

82481 
82  495 
82  509 
82  523 
82  537 

82  551 
9 

log  001 


log  tan 

9 

93916 
93942 

93  %7 

93  993 
94018 

94044 
94069 

94  095 
94120 
94146 

94171 
94197 
94  222 
94  248 
94  273 

94  299 
94324 
94  350 
94  375 
94  401 

94426 
94  452 
94  477 
94  503 
94  528 

94  554 
94  579 
94604 
94  630 
94655 

94  681 
94  706 
94  732 
94  757 
94  783 

94  808 
94  834 
94859 
94  884 
94910 

94935 

94  %1 
94986 

95  012 
95  037 

95  062 
95  088 
95113 
95139 
95164 

95190 
95  215 
95  240 
95  266 
95  291 

95  317 
95  342 
95  368 
95  393 
95  418 

95  444 
9 

log  oot 


logoot 

10 

06084 
06058 
06  033 
06007 
05  982 

05  956 
05  931 
05  905 
05  880 
05  854 

05  829 
05  803 
05  778 
05  752 
05  727 

05  701 
05  676 
05  650 
05  625 
05  599 

05  574 
05  548 
05  523 
05  497 
05  472 

05  446 
05  421 
05  3% 
05  370 
05  345 

05  319 
05  294 
05  268 
05  243 
05  217 

05192 
05166 
05141 
05116 
05  090 

05  065 
05  039 
05  014 
-04988 
04963 

04  938 
04912 
04  887 
04  861 
04  836 

04  810 
04  785 
04  760 
04  734 
04  709 

04  683 
04658 
04  632 
04  607 
04  582 

04  556 
lO 

log  too 


log  001 

9 

87  778 
87  767 

87  756 
87  745 
87  734 

87  723 
87  712 
87  701 
87  690 
87  679 

87  668 
87  657 
87  646 

87  635 
87  624 

87613 
87  601 
87  590 
87  579 
87  568 

87  557 
87  546 
87  535 
87  524 
87  513 

87  501 
87  490 
87  479 
87  468 
87  457 

87446 
87  434 
87423 
87  412 
87  401 

87390 
87  378 
87  367 
87  356 
87  345 

87  334 

87  322 
87  311 
87  300 
87  288 

87  277 
87  266 
87  255 
87  243 
87  232 

87  221 
87  209 
87198 
87  187 
87175 

87164 
87153 
87141 
87130 
87119 

87107 

9 
logiim 


00 

59 

58 
57 
56 

55 

54 
53 
52 
51 

50 

49 
48 
47 
46 

45 

44 
43 
42 
41 

40 

39 
38 
37 
36 

35 

34 
33 
32 
31 

30 

29 
28 
27 
26 

25 

24 
23 
22 
21 

20 

19 
18 
17 
16 

15 

14 
13 
12 
11 

10 

9 
8 
7 
6 

5 

4 
3 
2 
1 

O 


O 

1 
2 
3 
4 

5 

6 
7 
8 
9 

lO 

11 
12 
13 
14 

15 

16 
17 
18 
19 

20 

21 
22 
23 
24 

25 

26 
27 
28 
29 

30 

31 
32 
33 
34 

35 

36 
37 
38 
39 

40 

41 
42 
43 
44 

45 

46 
47 
48 
49 

50 

51 
52 
53 
54 

55 

56 
57 
58 
59 

60 


log  sin 

9 

82  551 
82  565 
82  579 
82  593 
82  607 

82  621 

82  635 
82  649 
82  663 
82  677 

82  691 
82  705 
82  719 
82  733 
82  747 
82  761 
82  775 
82  788 
82  802 
82  816 

82  830 
82  844 
82  858 
82  872 
82  885 

82  899 
82  913 
82  927 
82  941 
82955 

82968 
82  982 

82  9% 

83  010 
83  023 

83  037 
83  051 
83  065 
83  078 
83  092 

83106 
83120 
83133 
83147 
83161 

83174 
83188 
83  202 
83  215 
83  229 

83  242 
83  256 
83  270 
83  283 
83  297 

83  310 
83  324 
83  338 
83  351 
83  365 
83  378 
9 

log  001 


log  tan 

9 

95  444 
95  469 
95  495 
95  520 
95  545 

95  571 
95  5% 
95  622 
95  647 
95  672 

95  698 
95  723 
95  748 
95  774 
95  799 

95  825 
95  850 
95  875 
95  901 
95  926 

95  952 
95  977 
%002 
%028 
%053 

%078 
%104 
%129 
%155 
%180 

%205 
%231 
%256 
%281 
%307 

%332 
%357 
%383 
%408 
%433 

%459 
%484 
%510 
%535 
%560 

%586 
%611 
%636 
%662 
%687 

%712 
%738 
%763 
%788 
%814 

%839 
%864 
%890 
%915 
%940 

%966 
9 

logoot 


log  cot 

lO 

04  556 
04  531 
04  505 
04  480 
04  455 

04429 
04  404 
04  378 
04  353 
04328 

04  302 
04  277 
04  252 
04  226 
04  201 

04175 
04150 
04125 
04  099 
04074 

04048 
04  023 
03  998 
03  972 
03  947 

03  922 
03  8% 
03  871 
03  845 
03  820 

03  795 
03  769 
03  744 
03  719 
03  693 

03  668 
03  643 
03  617 
03  592 
03  567 

03  541 
03  516 
03  490 
03  465 
03  440 

03  414 
03  389 
03  364 
03  338 
03313 

03  288 
03  262 
03  237 
03  212 
03186 

03161 
03136 
03  110 
03  085 
03  060 

03  034 
lO 

log  tan 


log  008 

9 

87107 
87  0% 
87  085 
87  073 
87  062 

87  050 
87  039 
87  028 
87  016 
87  005 
86993 
86982 
86970 
86959 
86947 

86936 

86924 
86913 
86902 
86  890 

86879 
86867 
86  855 
86844 
86832 

86821 
86809 
86  798 
86  786 
86  775 
86  763 
86  752 
86  740 
86  728 
86  717 

86  705 
86  694 
86682 
86  670 
86659 

86647 
86635 
86624 
86612 
86600 

86  589 
86  577 
86  565 
86554 
86  542 

86  530 
86  518 
86  507 
86495 
86483 

86  472 
86  460 
86  448 
86436 
86425 
86413 

9 

log  sin 


60 

59 
58 
57 
56 

55 

54 
53 
52 
51 

50 

49 
48 
47 
46 

45 

44 
43 
42 
41 

40 

39 
38 
37 
36 

35 

34 
33 
32 
31 

30 

29 
28 
27 
26 

25 

24 
23 
22 
21 

20 

19 
18 
17 
16 

15 

-14 
13 
12 
11 

10 

9 
8 
7 
6 

5 

4 
3 
2 
1 

O 


> 


J 


r 

log  sin 

log  tan 

log  oot 

log  001 

f 

9 

83  378 

9 

96966 

lO 

03  034 

9 

86413 

O 

60 

1 

83  392 

96991 

03  009 

86  401 

59 

2 

83  405 

97  016 

02  984 

86389 

58 

3 

83  419 

97  042 

02  958 

86377 

57 

4 

83  432 

97  067 

02933 

86366 

56 

5 

83  446 

97  092 

02  908 

86354 

55 

6 

83  459 

97118 

02  882 

86342 

54 

7 

83  473 

97143 

02  857 

86330 

53 

8 

83  486 

97168 

02  832 

86318 

52 

9 

83  500 

97193 

02  807 

86306 

51 

lO 

83  513 

97  219 

02  781 

86  295 

50 

11 

83  527. 

97  244 

02  756 

86  283 

49 

12 

83  540 

97  269 

02  731 

86  271 

48 

13 

83  554 

97  295 

02  705 

86259 

47 

14 

83  567 

97  320 

02  680 

86  247 

46 

15 

83  581 

97345 

02  655 

86235 

45 

16 

83  594 

97  371 

02  629 

86  223 

44 

17 

83  608 

97  3% 

02  604 

86211 

43 

18 

83  621 

97  421 

02  579 

86  200 

42 

19 

83  634 

97  447 

02  553 

86188 

41 

20 

83  648 

97  472 

02  528 

86176 

40 

21 

83  661 

97  497 

02  503 

86164 

39 

22 

83  674 

97  523 

02  477 

86152 

38 

23 

83  688 

97  548 

02  452 

86140 

37 

24 

83  701 

97  573 

02  427 

86128 

36 

25 

83  715 

97  598 

02  402 

86116 

35 

26 

83728 

97  624 

02  376 

86104 

34 

27 

83  741 

97  649 

02  351 

86092 

33 

28 

83  755 

97  674 

02  326 

86080 

32 

29 

83  768 

97  700 

02  300 

86068 

31 

30 

83  781 

97  725 

02  275 

86056 

30 

31 

83  795 

97  750 

02  250 

86044 

29 

32 

83  808 

97  776 

02  224 

86032 

28 

33 

83  821 

97  801 

02199 

86020 

27 

34 

83  834 

97  826 

02174 

86008 

26 

35 

83848 

97  851 

02  149 

85  9% 

25 

36 

83  861 

97  877 

02123 

85  984 

24 

37 

83  874 

97  902 

02  098 

85  972 

23 

38 

83  887 

97  927 

02  073 

85  960 

22 

39 

83  901 

97953 

02047 

85  948 

21 

40 

83  914 

97  978 

02022 

85  936 

20 

41 

83  927 

98003 

01997 

85  924 

19 

42 

83  940 

98029 

01971 

85  912 

18 

43 

83  954 

98054 

01946 

85  900 

17 

44 

83  %7 

98079 

01921 

85  888 

16 

45 

83  980 

98104 

018% 

85  876 

15 

46 

83  993 

98130 

01870 

85  864 

14 

47 

84006 

98155 

01845 

85  851 

13 

48 

84020 

98180 

01820 

85  839 

12 

49 

84033 

98206 

01794 

85  827 

11 

50 

84  046 

98  231 

01769 

85  815 

io 

51 

84  059 

98  256 

01744 

85  803 

9 

52 

84072 

98  281 

01719 

85  791 

8 

53 

84  085 

98  307 

01693 

85  779 

7 

54 

84  098 

98  332 

01668 

85  766 

6 

55 

84112 

98  357 

01643 

85  754 

5 

56 

84125 

98  383 

01617 

85  742 

4 

57 

84138 

98408 

01592 

85  730 

3 

58 

84151 

98433 

01567 

85  718 

2 

59 

84164 

98458 

01542 

85  706 

1 

60 

84177 

98484 

01516 

85  693 

O 

9 

logOOB 

9 

logoot 

lO 

log  tan 

9 

log  sin 

1 

f 

J 

440 

49 

f 

log  tin 

log  tan  log  oot 

logoot 

f 

9 

84177 

9    10 

98484  01516 

9 

85  693 

0 

60 

1 

84190 

98  509  01491 

85  681 

59 

2 

84  203 

98  534  01466 

85  669 

58 

3 

84  216 

98  560  01440 

85  657 

57 

4 

84  229 

98  585  01415 

85  645 

56 

5 

84  242 

98610  01390 

85  632 

55 

6 

84  255 

98635  01365 

85  620 

54 

7 

84  269 

98661  01339 

85  608 

53 

8 

84  282 

98686  01314 

85  5% 

52 

9 

84  295 

98  711  01289 

85  583 

51 

10 

84  308 

98  737  01263 

85  571 

50 

11 

84321 

98  762  01238 

85  559 

49 

12 

84334 

98  787  01213 

85  547 

48 

13 

84347 

98  812  01188 

85  534 

47 

14 

84360 

98838  01162 

85  522 

46 

15 

84373 

98863  01137 

85  510 

45 

16 

84  385 

98  888  01112 

85  497 

44 

17 

84  398 

98913  01087 

85  485 

43 

18 

84  411 

98939  01061 

85  473 

42 

19 

84424 

98964  01036 

85  460 

41 

20 

84437 

98989  01011 

85  448 

40 

21 

84  450 

99015  00985 

85  436 

39 

22 

84  463 

99040  00960 

85  423 

38 

23 

84476 

99065  00935 

85  411 

37 

24 

84489 

99090  00910 

85  399 

36 

25 

84  502 

99116  00884 

85  386 

35 

26 

84  515 

99141  00859 

85  374 

34 

27 

84  528 

99166  00834 

85  361 

33 

28 

84  540 

99191  00809 

85  349 

32 

29 

84  553 

99217  00  783 

85  337 

31 

30 

84  566 

99  242  00  758 

85  324 

30 

31 

84  579 

99  267  00  733 

85  312 

29 

32 

84  592 

99293  00707 

85  29^ 

28 

33 

84605 

99318  00682 

85  287 

27 

34 

84618 

99343  00657 

85  274 

26 

35 

84  630 

99368  00632 

85  262 

25 

36 

84643 

99394  00606 

85  250 

24 

37 

84656 

99419  00581 

85  237 

23 

38 

84669 

99444  .00556 

85  225 

22 

39 

84682 

99469  00531 

.85  212 

21 

40 

84  694 

99495  00  505 

85  200 

20 

41 

84  707 

99520  00480 

85187 

19 

42 

84  720 

99  545  00455 

85175 

18 

43 

84  733 

99  570  00430 

85162 

17 

44 

84  745 

995%  00404 

85150 

16 

45 

84  758 

99621  00379 

85  137 

15 

46 

84  771 

99646  00354 

85125 

14 

47 

84  784 

99672  -00328 

85112 

13 

48 

84  7% 

99697  00303 

85100 

12 

49 

84809 

99  722  00278 

85067 

11 

50 

84  822 

99  747  00253 

85  074 

10 

51 

84  835 

99773  00227 

85  062 

9 

52 

84847 

99798  00202 

85  049 

8 

53 

84  860 

99823  00177 

85  037. 

7' 

54 

84  873 

99848  00152 

85  024 

6 

55 

84  885 

99874  00126 

85  012 

5 

56 

84898 

99899  00101 

84  999 

4 

57 

84  911 

99924  00076 

84  986 

3 

58 

84923 

99949  00051 

84  974 

2 

59 

84936 

99975  00025 

84  %1 

1 

60 

84  949 

8TO5B  00000 

84949 

0 

9 

10     10 

9 

f 

log  COS 

log  oot  log  tan 

logtln 

r 

48' 


47° 


46' 


45< 


-N 


II 


ii^MiCiittliSIlK^^^    ■■iiiiiiiiii3B3ill 


\y 


50 


TABLE  IV. 


For  Determining  with  Greater  Accuracy  than  can  be  done  by 

MEANS  OF  Table  III.: 

1.  log  sirif  log  taUf  and  log  cot,  when  tlio  angle  is  between  0**  and  2*; 

2.  log  cosj  log  tan,  and  log  cot,  when  the  angle  is  between  88°  and  90° ; 

3.  The  value  of  the  angle  when  the  logarithm  of  the  function  does  not 

lie  between  the  limits  8.  64  684  and  11. 46  316. 


FORMULAS  FOR  THE  USE  OF  THE  NUMBERS  S  AND  T. 

I.   When  the  angle  a  is  between  0°  and  2° : 

log  o"  =  log  sin  a^  S, 


log  sin  a  =  log  a"  +  S, 
log  tan  a  =  log  a"  +  T. 
log  cot  a  =  colog  tan  a. 


=  log  tan  a  —  2\ 
=  colog  cot  a—  T. 


II.   When  the  angle  a  is  between  88°  and  90° : 


log  cos  o  =  log  (90®  -  a)"  4-  S. 
log  cot  a  =  log  (90°  -  a)"  +  T. 
log  tan  a  =  colog  cot  a. 


log  (90°  -  a)"  =  log  cos  a  -  iS^, 
=  log  cot  a  —  T, 

zs  colog  tan  a  —  Tj 
aiido  =  90O-(90O-o). 


•  cCtc 


Yaltjes  of  S  and  T. 


0 

2409 
3417 
3  823 
4190 
4840 
5  414 
5  932 
6408 
6633 
6851 
7  267 


B 

4.68  557 
4.68  556 
4.68  555 
4.68  555 
4.68  554 
4. 68  553 
4.68  552 
4.68  551 
4.68550 
4.68  550 
4.  68  549 

8 


log  lin  a 

8.06  740 
8. 21 920 
8.  26  795 

8.30  776 

* 

8.37038 
8.41904 
8.45  872 

8.49  223 

8. 50  721 
S.  52  125 
8.54  684 

log  tin  « 


0 

200 
1726 

2  432 
2976 
3434 

3  838 
4204 

4  540 
4699 
4  853 
5146 


4.68  557 
4.68558 
4.68  559 
4.68  560 
4.68  561 
4.68  562 
4.68563 
4.68  564 
4.68  565 
4. 68  565 
4.68  566 


.#/ 


logtaaa 

6.98  660 
7.92  263 
8.07156 
8. 15  924 
8.  22  142 
8.26973 
8.30930 

8. 34  270 

8. 35  766 
8. 37  167 
8.39  713 

log  tan  a 


5146 
5  424 
5689 

5  941 
6184 
6417 
6642 

6  859 
7070 
7173 

7  274 


4. 68  567 
4.68  568 
4.68  569 
4.68  570 
4.68  571 
4. 68  572 
4.68573 
4.68  574 
4.68  575 
4.68  575 


log  tan  a 

8.39  713 
8.41999 

8.44  072 

8. 45  955 
8.47  697 
8.49305 
8.50  802 
8.  52  200 

8. 53  516 

8. 54  145 
8.54  753 

log  tana 


J 


«lta 


TABLE  v.— Circumferences  and  Areas  of  Circles,  si 


If  iV=  the  radius  of  the  circle 

,  the  circumference  =  2  rlf. 

, 

UN  =  the  radius  of  the  circle 

),  the  area 

=  iri\r«. 

If  iV  =  the  circumference  of  the  circle,  the  radius  =  -— 

2r 

N. 

If  iV  =  the  circumference  of  the  circle,  the  area     =  -— 

4ir 

iV". 

1 

K 

2rW          ' 'KN* 

aoo        0.0 

6. 28            3. 1 
12. 57          12. 6 
18.85          28.3 
25. 13          50. 3 

2ir 

0.000 
0.159 
0.318 
0.477 
0.637 

0.00 

0.08 
0.32 
0.72 
1.27 

N 

2vy 

314. 16 
320. 44 
326. 73 
333.01 
339.29 

7  854 
8171 
8495 

8  825 
9161 

2w 

7.96 
8.12 
8.28 
8.44 
8.59 

4» 

198.94 
206.98 
215. 18 
223.53 
232.05 

0 

1 
2 
3 
4 

50 

51 
52 
53 
54 

5 

6 
7 
8 
9 

31.42          78.5 
37. 70        113. 1 
43.98        153.9 
50. 27        2bl.  1 
56.55        254.5 

0.796 
0.955 
1.114 
1.273 
1.432 

1.99 

2.86 
3.90 
5.09 
6.45 

55 

56 
57 
58 
59 

345.58 
351.86 
358. 14 
364.42 
370.  71 

9  503 

9852 

10  207 

10568 

10936 

8.75 
8.91 
9.07 
9.23 
9.39 

240.  72 
249.55 
258. 55 
267.70 
277.01 

10 

11 
12 
13 
14 

62.83        314.2 
69. 12        380. 1 
75. 40        452. 4 
81. 68        530. 9 
87.96        615.8 

1.592 
1.751 
1.910 
2.069 
2.228 

7.96 

9.63 

11.46 

13.45 

15.60 

60 

61 
62 
63 
64 

376.99 
383.27 
389.56 
395.84 
402.12 

11310 
11690 
12076 
12  469 
12  868 

9.55 

9.71 

9.87 

10.03 

10.19 

286.48 
296.11 
305. 90 
315.84 
325.95 

15 

16 
17 
18 
19 

94. 25        706. 9 
100. 53        804.  2 
106. 81        907. 9 
113.10      1017.9 
119.38      1134.1 

2.387 
2.546 
2.706 
2.865 
3.024 

17.90 
20.37 
23.00 
25.78 
28.73 

65 

66 
67 
68 
69 

408.41 
414.69 
420. 97 
427.  26 
433. 54 

13  273 

13  685 
14103 

14  527 
14957 

10.35 
10. 50 
10.66 
10.82 
10.98 

336. 21 
346.64 

357. 22 
367.97 
378. 87 

20 

21 
22 
23 
24 

125. 66     1  256. 6 
131.95      1385.4 
138.  23      1 520.  5 
144. 51     1 661. 9 
150.80     1809.6 

3.183 
3. 342 
3.501 
3.661 
3.820 

31.83 
35.09 
38.52 
42.10 
45.84 

70 

71 
72 
73 
74 

439. 82 
446. 11 
452.39 
458. 67 
464.96 

15  394 

15  837 

16  286 

16  742 

17  203 

11.14 
11.30 
11.46 
11.62 
11.78 

389.93 
401. 15 
412.  53 
424.07 
435. 77 

25 

26 
27 

28 
29 

157.08     1963.5 
163. 36     2 123.  7 
169. 65     2  290. 2 
175.93     2463.0 
182.21      2642.1 

3.979 
4. 138 
4.297 
4.456 
4.615 

49.74 
53.79 
58.01 
62.39 
66.92 

75 

76 
77 
78 
79 

471. 24 
477.52 
483.81 
490.09 
496.37 

17671 
18146 
18627 
19113 
19607 

11.94 
12.10 
12.25 
12.41 
12.57 

447.62 
459.64 
471. 81 
484.15 
4%.  64 

30 

31 
32 
33 
34 

188.50     2  827.4 
194.78     3  019.1 
201. 06     3  217. 0 
207.35     3  421.2 
213.63     3  631.7 

4.775 
4.934 
5.093 
5.252 
5.411 

71.62 
76.47 
81.49 
86.66 
91.99 

80 

81 
82 
83 
84 

502.65 
508.94 
515. 22 
521. 50 
527.  79 

20106 
20612 
21124 
21642 
22167 

12.73 
12.89 
13.05 
13.21 
13.37 

509.30 
522. 11 
535.08 
548. 21 
561'.  50 

35 

36 
37 
38 
39 

219.91     3  848.5 
226.19     4071.5 
232.48     4300.8 
238.76     4  536.5 
245.04     4  778.4 

5.570 
5.730 
5.889 
6.048 
6.207 

97.48 
103. 13 
108.94 
114.91 
121.04 

85 

86 
87 
88 
89 

534.07 
540.35 
546.64 
552.92 
559.20 

22  698 

23  235 

23  779 

24  328 
24885 

13.53 
13.69 

13.85 
14.01 
14.16 

574. 95 
588.55 
602.32 
616. 25 
630.33 

40 

41 
42 
43 
44 

251.33     5  026.5 
257. 61     5  281. 0 
263. 89     5  541. 8 
270.18     5  808.8 
276.46     6082.1 

6.366 
6.525 

6.685 
6.844 
7.003 

127.32 
133. 77 
140.37 
147. 14 
154.06 

90 

91 
92 
93 
94 

565.49 
571. 77 
578. 05 
584.34 
590.62 

25447 
26016 

26  590 
27172 

27  759 

14.32 
14.48 
14.64 
14.80 
14.% 

644.58 
658.98 
673. 54 
688.27 
703. 15 

45 

46 
47 
48 
49 

282.74     6361.7 
289.03      6647.6 
295.31      6939.8 
301. 59      7  238. 2 
307. 88      7  543. 0 

7.162 
7.321 
7.480 
7.639 
7.799 

161. 14 
168.39 
175. 79 
183.35 
191.07 

95 

96 
97 
98 
99 

5%.  90 
603.19 
609.47 
615.75 
622.04 

28353 
28953 

29  559 
30172 

30  791 

15.12 
.15.28 
15.44 
15.60 
15.76 

718.19 
733. 39 
748.  74 
764.26 
779.94 

50 

314.16      7  854.0 
2iriV            vlf* 

7.958 
2ir 

198.94 
4r 

100 

628.32 

31416 

15.92 

2x 

795.  77 

4X 

F 

N 

4 


f.  1 


f 


1 

62 

TABLE  VL-I^ 

i<'UNCTIONS. 

ATUML 

/ 

o° 

1° 

2° 

3° 

4° 

f 

sin  cos 

sin  cos 

sin  cos 

sin  cos 

sin  cos 

^1 

0 

0000  1.000 

0175  9998 

0349  9994 

0523  9986 

0698  9976 

60 

^H 

1 

0003  1.000 

0177  9998 

0352  9994 

0526  9986 

0700  9975 

59 

^1 

2 

0006  1.000 

0180  9998 

0355  9994 

0529  9986 

0703  9975 

58 

^H 

3 

0009  1.000 

0183  9998 

0358  9994 

0532  9986 

0706  9975 

57 

II 

4 

0012  .1.000 

0186  9998 

0361  9993 

0535  9986 

0709  9975 

56 

II 

5 

0015  1.000 

0189  9998 

0364  9993 

0538  9986 

0712  9975 

55 

1 

6 

0017  1.000 

0192  9998 

0366  9993 

0541  9985 

0715  9974 

54 

1 

7 

0020  1.000 

0195  9998 

0369  9993 

0544  9985 

0718  9974 

53 

1 

8 

0023  1.000 

0198  9998 

0372  9993 

0547  9985 

0721  9974 

52 

1 

9 

0026  1.000 

0201  9998 

0375  9993 

0550  9985 

0724  9974 

51 

1 

10 

0029  1.000 

0204  9998 

0378  9993 

0552  9985 

0727  9974 

50 

1 

11 

0032  1.000 

0207  9998 

0381  9993 

0555  9985 

0729  9973 

49 

1 

12 

0035  1.000 

0209  9998 

0384  9993 

0558  9984 

0732  9973 

48 

1 

13 

0038  1.000 

0212  9998 

0387  9993 

0561  9984 

0735  9973 

47 

1 

14 

0041  1.000 

0215  9998 

0390  9992 

0564  9984 

0738  9973 

46 

1 

15 

0044  1.000 

0218  9998 

0393  9992 

0567  9984 

0741  9973 

45 

1 

16 

0047  1.000 

0221  9998 

03%  9992 

0570  9984 

0744  9972 

44 

1 

17 

0049  1.000 

0224  9997 

0398  9992 

0573  9984 

0747  9972 

43 

1 

18 

0052  1.000 

0227^  9997 

0401  9992 

0576  9983 

0750  9972 

42 

1 

19 

0055  1.000 

0230  9997 

0404  9992 

0579  9983 

0753  9972 

41 

1 

20 

0058  1.000 

0233  9997 

0407  9992 

0581  9983 

0756  9971 

40 

1 

21 

0061  1.000 

0236  9997 

0410  9992 

0584  9983 

0758  9971 

39 

1 

22 

0064  1.000 

0239  9997 

0413  9991 

0587  9983 

0761  9971 

38 

'  1 

23 

0067  1.000 

0241  9997 

0416  9991 

0590  9983 

0764  9971 

37 

I  1 

24 

0070  1.000 

0244  9997 

0419  9991 

0593  9982 

0767  9971 

36 

1  1 

25 

0073  1.000 

0247  9997 

0422  9991 

05%  9982 

0770  9970 

35 

H  1 

26 

0076  1.000 

0250  9997 

0425  9991 

0599  9982 

0773  9970 

34 

ij  1 

27 

.0079  1.000 

0253  9997 

0427  9991 

0602  9982 

0776  9970 

33 

n  1 

28 

0081  1.000 

0256  9997 

0430  9991 . 

0605  9982 

0779  9970 

32 

1  w 

29 

0084  1.000 

0259  9997 

0433  9991 

0608  9982 

0782  9%9 

31 

1  1 

30 

0087  1.000 

0262  9997 

0436  9990 

•  0610  9981 

0785  9%9 

30 

1  ; 

31 

0090  1.000 

0265  99% 

0439  9990 

0613  9981 

0787  9%9 

29 

32 

0093  1.000 

0268  9996 

0442  9990 

0616  9981 

0790  9%9 

28 

» 

33 

0096  1.000 

0270  99% 

0445  9990 

0619  9981 

0793  9968 

27 

II 

1         34 

0099  1.000 

0273  99% 

0H8  9990 

0622  9981 

07%  9968 

26 

1 

35 

0102  9999 

0276  99% 

0451  9990 

0625  9980 

0799  9968 

25 

f         36 

0105  9999 

0279  99% 

0454  9990 

0628  9980 

0802  9968 

24 

.  r 

37 

0108  9999 

0282  99% 

0457  9990 

0631  9980 

0805  9968 

23 

■ 

38 

0111  9999 

0285  99% 

0459  9989 

0634  9980 

0808  9%7 

22 

(1 

'  r  ' 

39 

0113  9999 

0288  99% 

0462  9989 

0637  9980 

0811  9%7 

21 

40 

0116  9999 

0291  99% 

0465  9989 

0640  9980 

0814  9%7 

20 

41 

0119  9999 

0294  99% 

0468  9989 

0642  9979 

0816  9%7 

19 

42 

0122  9999 

0297  99% 

0471  9989 

0645  9979 

0819  9966 

18 

43  , 

0125  9999 

0300  99% 

0474  9989 

0648  9979 

0822  9966  . 

17 

''■ 

44 

0128  9999 

0302  9995 

0477  9989 

0651  9979 

0825  9966 

16 

[  !■ 

45 

0131  9999 

0305  9995 

0480  9988 

0654  9979 

0828  9966 

15 

ill 

46 

0134  9999 

0308  9995 

0483  9988 

0657  9978 

0831  9%5 

14 

III 

47 

0137  9999 

0311  9995 

0486  99B8 

0660  9978 

0834  9%5 

13' 

iM 

48 

0140  9999 

0314  9995 

0488  9988 

0663  9978 

0837  9%5 

12 

■| 

49 

0143  9999 

0317  9995 

0491  9988 

0666  9978 

0840  9%5 

11 

II 

50 

0145  9999 

0320  9995 

0494  9988 

0669  9978 

0843  9964 

lO 

m 

51 

0148  9999 

0323  95^5 

0497  9988 

0671  9977 

0845  9964 

9 

1  ii 

52 

0151  9999 

0326  9995 

0500  9987 

0674  9977 

0848  9964 

8 

1  T 

53 

0154  9999 

0329  9995 

0503  9987 

0677  9977 

0851  9964 

7 

Ui 

54 

0157  9999 

0332  9995 

0506  9987 

0680  9977 

0854  9963 

6 

55 

0160  9999 

0334  9994 

0509  9987 

0683  9977 

0857  9963 

5 

1  , 

56 

0163  9999 

0337  9994 

0512  9987 

0686  9976 

0860  9%3 

4 

57 

0166  9999 

0340  9994 

0515  9987 

0689  9976 

0863  9963 

3 

. 

58 

0169  9999 

0343  9994 

0518  9987 

0692  9976 

0866  9%2 

2 

ik 

59 

0172  9999 

0346  9994 

0520  9986 

0695  9976 

0869  9%2 

1 

M 

60 

0175  9999 

0349  9994 

.  0523  9986 

0698  9976 

0872  9%2 

O 

i 

cos  sin 
89° 

cos  sin 
88° 

cos  sin 
87° 

cos.  sin 
86° 

cos  sin 
85° 

f 

f 

K 

1 

wtmtumtmm 


NATURAL  SINES   AND  COSINES. 


58 


i 

f 

5° 

6° 

7° 

8° 

9° 

t 

'         * 

sin  cos 

sin  cos 

sin  cos 

sin  cos 

sin  cos 

0 

0872  9%2 

1045  9945 

1219  9925 

1392  9903 

1564  9877 

60 

1 

0874  9%2 

1048  9945 

1222  9925 

1395  9902 

1567  9876 

59 

^ 

2 

0877  9%1 

1051  9945 

1224  9925 

1397  9902 

1570  9876 

58 

3 

0880  9%i 

1054  9944 

1227  9924 

1400  9901 

1573  9876 

57 

« 

4 

0883  9%1 

1057  9944 

1230  9924 

1403  9901 

1576  9875 

56 

5 

0886  9%1 

1060  9944 

1233  9924 

1406  9901 

1579  9875 

55 

. 

6 

0889  9960 

1063  9943 

1236  9923 

1409  9900 

1582  9874 

54 

7 

0892  9960 

1066  9943 

1239  9923 

1412  9900 

1584  9874 

53 

8 

0895  9960 

1068  9943 

1241  9923 

1415  9899 

1587  9873 

52 

. 

9 

0898  9960 

1071  9942 

1245  9922 

1418  9899 

1590  9873 

51 

lO 

0901  9959 

1074  9942 

1248  9922 

1421  9899 

1593  9872 

50 

. 

11 

0903  9959 

1077  9942 

1250  9922 

1423  9898 

15%  9872 

49 

-',       1 

12 

0906  9959 

1080  9942 

1253  9921 

1426  9898 

1599  9871 

v^ 

13 

0909  9959 

1083  9941 

1^56  9921 

1429  9897 

1602  9871  -' 

14 

0912  9S>58 

1086  9941 

1259  9920 

1432  9897 

1605  9870' 

46 

15 

0915  9958 

1089  9941 

1262  9920 

1435  9897 

1607  9870 

1? 

16 

0918  9958 

1092  9940 

1265  9920 

1438  98% 

1610  9869 

44 

* 

17 

0921  9958 

1094  9940 

1268  9919 

1441  98% 

1613  9669 

43 

1 

18 

0924  9957 

1097  9940 

1271  9919 

1444  9895 

1616  9869 

42 

19 

0927  9957 

1100  9939 

1274  9919 

1446  9895 

1619  9868 

41 

20 

0929  9957 

1103  9939 

1276  9918 

1449  9894 

1622  9868 

40 

21 

0932  9956 

1106  9939 

1279  9918 

1452  9894 

1625  9867 

39 

. 

22 

0935  9956 

1109  9938 

1282  9917 

1455  9894 

1628  9867 

38 

; 

, 

23 

0938  9956 

1112  9938 

1285  9917 

1458  9893 

1630  9866 

37 

»  . 

24 

0941  9956 

1115  9938 

1288  9917 

1461  9893 

1633  9866 

36  J, 

^ 

25 

0944  9955 

1118  9937 

1291  9916 

1464  9892 

1636  9865 

35 

26 

0947  9955 

1120  9937 

1294  9916 

1467  9892 

1639  9865 

34 

'\'^ 

27 

0950  9955 

1123  9937 

1297  9916 

1469  9891 

1642  9864 

33 

28 

0953  9955 

1126  9936 

1299  9915 

1472  9891 

1645  9864 

32 

• 

29 

0956  9954 

1129  9936 

1302  9915 

1475  9891 

1648  9863 

31 

30 

0958  9954 

1132  9936 

1305  9914 

1478  9890 

1650  9863 

30 

31 

0%1  9954 

1135  9935 

1308  9914 

1481  9890 

1653  9862 

29 

32 

0964  9953 

1138  9935 

1311  9914 

1484  9889 

1655  9862 

28 

33 

0%7  9953 

1141  9935 

1314  9913 

1487  9889 

1659  9861 

27 

34' 

0970  9953 

1144  9934 

1317  9913 

1490  9888 

1662  9661 

26 

35 

0973  9953 

1146  9934 

1320  9913 

1492  9888 

1665  9860 

25 

36 

0976  9952 

1149  9934 

1323  9912 

1495  9888 

1668  9860 

24 

« 

37 

0979  9952 

1152  9933 

1325  9912 

1498  9887 

1671  9859 

23 

• 

**  • 

38 

0982  9952 

1155  9933 

1328  9911 

1501  9887 

1673  9859 

22 

\' 

39 

0985  9951 

1158  9933 

1331  9911 

1504  9886 

1676  9859 

21 

( 

40 

0987  9951 

1161  9932 

1334  9911 

1507  9886 

1679  9858 

20 

1 

41 

0990  9951 

1164  9932 

1337  9910 

1510  9885 

1682  9858 

19 

-' 

42 

0993  9951 

1167  9932 

1340  9910 

1513  9885 

1685  9857 

18 

f'- 

43 

09%  9950- 

1170  9931 

1343  9909 

1515  9884 

1688  9857 

17 

44 

0999  9950 

1172  9931 

1346  9909 

1518  9884 

1691  9856 

16 

45 

1002  9950 

1175  9931 

1349  9909 

1521  9884 

1693  9856 

^? 

46 

1005  9949 

1178  9930 

1351  9908 

1524  9883 

16%  9855 

14 

47 

1008  9949 

1181  9930 

1354  9908 

1527  9883 

1699  9855 

13 

48 

1011  9949 

.1184  9930 

1357  9907 

1530  9882 

1702  9854 

12 

49 

1013  9949 

1187  9929 

1360  9907 

1533  9882 

1705  9854 

11 

50 

1016  9948 

1190  9929 

1363  9907 

1536  9881 

1708  9853 

lO 

51 

1019  9948 

1193  9929 

1366  9906 

1538  9881 

1711  9853 

9 

52 

1022  9948 

11%  9928 

1369  9906 

1541  9880 

1714  9852 

8 

53 

1025  9947 

1198  9928 

1372  9905 

1544  9880 

1716  9852 

7 

54 

1028  9947 

1201  9928 

1374^  9905 

1547  9880 

1719  9851 

6 

55 

1031  9947 

1204  9927 

1377  9905 

1550  9879 

1722  9851 

5 

56 

1034  9946 

1207  9927 

1380  9904 

1553  9879 

1725  9850 

4 

57 

1037  9946 

1210  9927 

1383  9904 

1556  9878 

1728  9850 

3 

58 

1039  9946 

1213  9926 

1386  9903 

1559  9878 

1731  9849 

2 

59 

1042  9946 

1216  9926 

1389  9903 

1561  9877 

1734  9849 

1 

'• 

60 

1045  9945 

1219  9925 

1392  9903 

1564  9877 

1736  9848 

O 

cos  sin 
84° 

cos  sin 
83° 

cos  sin 
82° 

cos  sin 
81° 

cos  sin 
80° 

\ 

p- 

f 

•• 

*  • 

\ 


u 


54 


NATURAL  SINES   AND   COSINES. 


/ 

10° 

11° 

12° 

13° 

14° 

f 

sin  cos 

sin  cos 

sin  cos 

sin  cos 

sin  cos 

a 

1736  9848 

1908  9816 

2079  9781 

2250  9744 

2419  9703 

60 

1 

1739  9848 

1911  9816 

2082  9781 

2252  9743 

2422  9702 

59 

2 

1742  9847 

1914  9815 

2085  9780 

2255  9742 

2425  9702 

58 

3 

1745  9847 

1917  9815 

2088  9780 

2258  9742 

2428  9701 

57 

4 

1748  9846 

1920  9814 

2090  9779 

2261  9741 

2431  9700 

56 

5 

1751  9846 

1922  9813 

2093  9778 

2264  9740 

2433  %99 

55 

6 

1754  9845 

1925  9813 

2096  9778 

2267  9740 

2436  %99 

54 

7 

1757  98-f5 

1928  9812 

209*;  9777 

2269  9739 

2439  9698 

53 

8 

1759  9844 

1931  9812 

2102  9777 

2272  9738 

2442  %97 

52 

9 

1762  9843 

1934  9811 

2105  9776 

2275  9738 

2445  %97 

51 

lO 

1765  9843 

1937  9811 

2108  9775 

2278  9737 

2447  %% 

60 

11 

1768  9842 

1939  9810 

2110  9775 

2281  9736 

2450  %95 

49 

12 

1771  9842 

1942  9810 

2113  9774 

2284  9736 

2453  %94 

48 

13 

1774  9841 

1945  9809 

2116  9774 

2286  9735 

2456  %94 

47 

14 

1777  9841 

1948  9808 

2119  9773 

2289  9734 

2459  %93 

46 

16 

1779  9840 

1951  9808 

2122  9772 

2292  9734 

2462  %92 

46 

16 

1782  9840 

1954  9807 

2125  9772 

2295  9733 

2464  %92 

44 

17 

1785  9839 

1957  9807 

2127  9771 

2298  9732 

2467  %91 

43 

18 

1788  9839 

1959  9806 

2130  9770 

2300  9732 

2470  9690 

42 

19 

1791  9838 

1%2  9806 

2133  9770 

2303  9731 

2473  9689 

41 

20 

1794  9838 

1%S  9805 

2136  9769 

2306  9730 

2476  9689 

40 

21 

1797  9837 

1968  9804 

2139  9769 

2309  9730 

2478  9688 

39 

22 

1799  9837 

1971  9804 

2142  9768 

2312  9729 

2481  9687 

38 

23 

1802  9836 

1974  9803 

2145  9767 

2315  9728 

2484  9687 

37 

24 

1805  9836 

1977  9803 

2147  9767 

2317  9728 

2487  9686 

36 

26 

1808  9835 

1979  9802 

2150  9766 

2320  9727 

2490  9685 

35 

26 

1811  9835 

1982  9802 

2153  9765 

2323  9726 

2493  9684 

34 

27 

1814  9834 

1985  9801 

2156  9765 

2326  9726 

2495  9684 

33 

28 

1817  9834 

1988  9800 

2159  9764 

2329  9725 

249^  9683 

32 

29 

1819  9833 

1991  9800 

2162  9764 

2332  9724 

2501  9682 

31 

30 

1822  9833 

1994  9799 

2164  9763 

2334  9724 

2504  9681 

30 

31 

1825  9832 

1997  9799 

2167  9762 

2337  9723 

2507  9681 

29 

32 

1828  9831 

1999  9798 

2170  9762 

2340  9722 

2509  9680 

,  28 

33 

1831  9831 

2002  9798 

2173  9761 

2343  9722 

2512  %79 

27 

34 

1834  9830 

2005  9797 

2176  9760 

2346  9721 

2515  9679 

26 

35 

1837  9830 

2008  9796 

2179  9760 

2349  9720 

2518  %78 

25 

36 

1840  9829 

2011  97% 

2181  9759 

2351  9720 

2521  %77 

24 

37 

1842  9829 

2014  9795 

2184  9759 

•  2354  9719 

2524  9676 

23 

38 

1845  9828 

2016  9795 

2187  9758 

2357  9718 

2526  9676 

22 

39 

1848  9828 

2019  9794 

2190  9757 

2360  9718 

2529  9675 

21 

40 

1851  9827 

2022  9793 

2193  9757 

2363  9717 

2532  %74 

20 

41 

1854  9827 

2025  9793 

2196  9756 

2366  9716 

2535  9673 

19 

42 

1857  9826 

2028  9792 

2198  9755 

2368  9715 

2538  %73 

18 

43 

1860  9826 

2031  9792 

2201  9755 

2371  9715 

2540  9672 

17 

44 

1862  9825 

2034  9791 

2204  9754 

2374  9714 

2543  9671 

16 

46 

1865  9825 

2036  9790 

2207  9753 

2377  9713 

2546  %70 

16 

46 

1868  9824 

2039  9790 

2210  9753 

2380  9713 

2549  9670 

14 

47 

1871  9823 

2042  9789 

2213  9752 

2383  9712 

2552  9669 

13 

48 

1874  9823 

2045  9789 

2215  9751 

2385  9711 

2554  9668 

12 

49 

1877  9822 

2048  9788 

2218  9751 

2388  9711 

2557  9667 

11 

60 

1880  9822 

2051  9787 

2221  9750 

2391  9710 

2560  9667 

lO 

51 

1882  9821 

2054  9787 

2224  9750 

2394  9709 

2563  9666 

9 

52 

1885  9821 

2056  9786 

2227  9749 

2397  9709 

2566  9665 

8 

53 

1888  9820 

2059  9786 

2230  9748 

2399  9708 

2569  9665 

7 

54 

1891  9820 

2062  9785 

2233  9748 

2402  9707 

2571  9664 

6 

66 

1894  9819 

2065  9784 

2235  9747 

2405  9706 

2574  9663 

6 

56 

1897  9818 

2068  9784 

2238  9746 

2408  9706 

2577  9662 

4 

57 

1900  9818 

2071  9783 

2241  9746 

2411  9705 

2580  9662 

3 

S8 

1902  9817 

2073  9783. 

2244  9745 

2414  9704 

2583  9661 

2 

59 

1905  9817 

2076  9782 

2247  9744 

2416  9704 

2585  9660 

1 

60 

1908  9816 

2079  9781 

2250  9744 

2419  9703 

2588  96^9 

O 

cos  sin 
79° 

cos  sin 
78° 

cos  sin 

77° 

cos  sin 
76° 

cos  sin' . 

76° 

f 

f 

4^ 

NATURAL 

SINES  AND 

COSINKS. 

55 

f 

sin  cos 

^16° 

sin  cos 

17° 

18° 

19° 

t 

sin  cos 

sin  cos 

sin  cos 

0 

2588  %59 

2756  9613 

2924  9563 

.3090  9511 

3256  9455 

60 

1 

2591  %5? 

2759  %12 

2926  9562 

3093  9510 

3258  9454 

59 

2 

2594  9618 

2762  9611 

2929  9561' 

30%  9509 

3261  9453 

58 

3 

2597  9657 

2165  9610 

2932  9560 

3098  9508 

3264  ,9452 

57 

4 

2599  .9656 

2768  9609 

2935  9560 

3101  9507 

3267  9451 

56 

6 

2602  9655 

2770  9609 

2938  9559 

3104  9506 

3269  9450 

65 

6 

2605  %5S 

2773  9608 

2940  9558 

3107  9505 

3272  9449 

54 

7 

2608  9654 

2776  9607 

2943  9557 

3110  9504 

3275  9449 

53 

8 

2611  9653  ■ 

2779  9606 

2946  9556 

3112  9503 

3278  9448 

52 

9 

2613.  %52 

2782  9605 

2949  9555 

3115  9502 

3280  9447 

51 

10 

2616  %52 

2784  9605 

2952  9555 

3118  9502 

3283  9446 

60 

11 

2619  %51 

2787  9604 

2954  9554 

3121  9501 

3286  9445 

49 

12 

2622  %50 

2790  9603 

2957  9553 

3123  9500 

3289  9444 

48 

13 

2625  9649 

2793  9602 

2960  '9552 

3126  9499 

3291  9443 

47 

14 

2628  9649 

2795  9601 

2963  9551 

3129  9498 

3294  9442 

46 

15 

2630  9648 

2798  9600 

2%5  9550 

3132  9497 

3297  9441 

46 

16 

2633  9647 

2801  9600 

2968  9549 

3134  94% 

3300  9440 

44 

17 

2636  9646 

2804  9599 

2971  9548 

3137  9495 

3302  9439 

43 

18 

2639  9646 

2807  9598 

2974  9548 

3140  9494 

3305  9438 

42 

19 

2642  9645 

2809  9597 

2977  9547 

3143  9493 

3308  9437 

41 

20 

2644  9644 

2812  9596 

2979  9546 

3145  9492 

3311  9436 

40 

21 

2647  9643 

2815  95% 

2982  9545 

3148  9492 

3313  9435 

52' 

22 

2650  9642 

2818  9595 

2985  9544 

3151  9491 

3316  9434 

38 

23 

2653  9642 

2821  9594 

2988  9543 

3154  9490 

3319  9433 

51  i 

24 

2656  9641 

2823  9593 

2990  9542 

3156  9489 

3322  9432 

36  ^ 

26 

2658  9640 

2826  9592 

2993  9542 

3159  9488 

3324  9431 

36 

26 

2661  9639 

2829  9591. 

29%  9541 

3162  9487 

3327  9430 

34  . 

27 

2664  9639 

2832  9591 

2999  9540 

3165  9486 

3330  9429 

33  » 

28 

2667  9638 

2835  9590 

3002  9539 

3168  9485 

3333  9428 

32 

29 

2670  9637 

2837  9589 

3004  9538 

3170  9484 

3335  9427 

31 

30 

2672  9636 

2840  9588 

3007  9537 

3173  9483 

3338  9426 

30 

r 

31 

2675  9636 

2843  9587 

3010  9536 

3176.9482 

3341  9425 

29  . 

32 

2678  9635 

2846  9587 

3013  9535 

3179  9481 

3344  9424 

28  • 

33 

2681  9634 

2849  9586 

3015  9535 

3181  9480 

3346  9423 

•  27 

34 

2684  9633 

2851  9585 

3018  9534 

3184  9480 

3349  9423 

26 

35 

2686  9632 

2854  9584 

3021  9533 

3187  9479 

3352  9422 

26 

36 

2689  9632 

2857  9583 

3024  9532 

3190  9478 

3355  -9421 

24 

37 

2692  9631 

2860  9582 

3026  9531 

3192  9477 

3357  9420 

23 

38 

2695  9630 

2862  9582 

3029  9530 

3195  9476 

3360  9419 

22 

39 

2698  9629 

2865  9581 

3032  9529 

3198  9475 

3363  9418 

21 

40 

2700  9628 

2868  9580  . 

3035  9528 

3201  9474 

3365  9417 

20 

41 

2703  9628 

2871  9579 

3038  0527 

3203  9473 

3368  9416 

19 

42 

2706  %27 

2874  9578 

3040  9527 

3206  9472 

3371  9415 

18 

43 

2709  %26 

2876  9577 

3043  9526 

3209  9471 

3374  9414 

17 

44 

2712  9625 

2879  9577 

3046  9525 

3212  9470 

3376  9413 

16 

46 

2714  9625 

2882  9576 

3049  9524 

3214  .9469 

3379  9412 

16 

46 

2717  9624 

2885  9575 

3051  9523 

3217  9468 

3382  .9411 

14 

47 

2720  %23 

2888  9574 

3054  9522 

3220  9467 

3385  ,9410 

13 

48 

2723  9622 

2890  9573 

3057  9521 

3223  9466 

3387  9409 

12 

49 

2726  %21 

2893  9572 

3060  9520 

3225  9466 

3390  9408 

11 

60 

2728  %21 

28%  9572 

3062.9520 

3228  9465 

3393  9407 

lO 

51 

2731  9620 

2899  9571 

3065  9519 

3231  9464 

33%  9406 

9 

52 

2734  %19 

2901  9570 

3068  9518 

3234  9463 

3398  9405 

8 

53 

2737  9618 

2904  9569 

3071  9517 

3236  9462 

3401  9KH 

7 

54 

2740  %17 

2907  9568 

3074  9516 

3239  9461 

3404  9403 

6 

66 

2742  9617 

2910  9567 

3076  9515 

3242  9460 

3407  9402 

6 

56 

2745  9616 

2913  9566 

'  3079  9514 

3245  9459 

3409  9401 

4 

57 

2748  9615 

2915  9566 

3082  9513 

3247  9458 

3412  9400 

3 

58 

2751  %14 

2918  9565 

3085  9512 

3250  9457 

3415  9399 

2 

59 

2754  9613 

2921  9564 

3087  9511 

.3253  9456 

3417  9398 

1 

60 

2756  %13 

2924  9563 

3090  9511 

3256  9455 

3420  9397 

O 

cos  sin 

74° 

cos  sin 
73° 

cos  sin 

72° 

cos  sin 
71° 

cos  sin 
70° 

f 

f 

I 

1 


i_l 


56 


NATURAL  SINES   AND   COSINES. 


NATURAL  SINES  AND  COSINES. 


/^ 


67 


/ 

20° 

sin  cos 

21° 

22° 

sin  COS 

23° 

sin  cos 

24° 

sin  cos 

f 

sin  cos 

o 

3420  9397 

3584  9336 

3746  9272 

3907  9205 

4067  9135 

60 

1 

3423  93% 

3586  9335 

3749  9271 

3910  9204 

4070  9134 

59 

2 

3426  9395 

3589  9334 

3751  9270 

3913  9203 

4073  9133 

58 

3 

3428  9394 

3592  9333 

3754  9269 

3915  9202 

4075  9132 

57 

4 

3431  9393 

3595  9332 

3757  9267 

3918  9200 

4078  9131 

56 

5 

3434  9392 

3597  9331 

3760  9266 

3921  9199 

4081  9130 

55 

6 

3437  9391 

3600  9330 

3762  9265 

3923  9198 

4083  9128 

54 

7 

3439  9390 

3603  9328 

3765  9264 

3926  9197 

4086  9127 

S3 

8 

3442  9389 

3605  9327 

3768  9263 

3929  91% 

4089  9126 

52 

9 

3445  9388 

3608  9326 

3770  9262 

3931  9195 

4091  9125 

51 

10 

3448  9387 

3611  9325 

3773  9261 

3934  9194 

4094  9124 

50 

11 

3450  9386 

3614  9324 

3776  9260 

3937  9192 

4097  9122 

49 

12 

3453  9385 

3616  9323 

3778  9259 

3939  9191 

4099  9121 

48 

13 

3456  9384 

3619  9322 

3781  9258 

3942  9190 

4102  9120 

47 

14 

3458  9383 

3622  9321 

3784  9257 

3945  9189 

4105  9119 

46 

15 

3461  9382 

3624  9320 

3786  9255 

3947  9188 

4107  9118 

45 

16 

3464  9381 

3627  9319 

3789  9254 

3950  9187 

4110  9116 

44 

17 

3467  9380 

3630  9318 

3792  9253 

3953  9186 

4112  9115 

43 

18 

3469  9379 

3633  9317 

3795  9252 

3955  9184 

4115  9114 

42 

19 

3472  9378 

3635  9316 

3797  9251 

3958  9183 

4118  9113 

41 

20 

3475  9377 

3638  9315 

3800  9250 

3%1  9182 

4120  9112 

40 

21 

3478  9376 

3641  9314 

3803  9249 

3963  9181 

4123  9110 

39 

22 

3480  9375 

3643  9313 

3805  9248 

3966  9180 

4126  9109 

38 

23 

3483  9374 

3646  9312 

3808  9247 

3%9  9179 

4128  9108 

37 

24 

3486  9373 

3649  9311 

3811  9245 

3971  9178 

4131  9107 

36 

25 

3488  9372 

3651  9309 

3813  9244 

3974  9176 

4134  9106 

35 

26 

3491  9371 

3654  9308 

3816  9243 

.  3977  9175 

4136  9104 

34 

27 

3494  9370 

3657  9307 

3819  9242 

3979  9174 

4139  9103 

33 

28 

3497  9369 

3660  9306 

3821  9241 

3982  9173 

4142  9102 

32 

29 

3499  9368 

3662  9305 

3824  9240 

3985  9172 

4144  9101 

31 

30 

3502  9367 

3665  9304 

3827  9239 

3987  9171 

4147  9100 

30 

31 

3505  9366 

3668  9303 

3830  9238 

3990  9169 

4150  9098 

29 

32 

3508  9365 

3670  9302 

3832  9237 

3993  9168 

4152  9097 

28 

33 

3510  9364 

3673  9301 

3835  9235 

3995  9167 

4155  90% 

27 

34 

3513  9363 

3676  9300 

3838  9234 

3998  9166 

4158  9095 

26 

35 

3516  9362 

3679  9299 

3840  9233 

4001  9165 

4160  9094 

25 

36 

3518  9361 

3681  9298 

3843  9232 

4003  9164 

.4163  9092 

24 

37 

3521  9360 

3684  9297 

3846  9231 

4006  9162 

<165  9091 

23 

38 

3524  9359 

3687  9296 

3848  923Q 

4009  9161 

4168  9090 

22 

39 

3527  9358 

3689  9295 

3851  9229 

4011  9160 

4171  9088 

21 

40 

3529  9356 

3692  9293 

3854  9228 

4014  9159 

4173  9088 

20 

41 

3532  9355 

3695  9292 

3856  9227 

4017  9158 

4176  9086 

19 

42 

3535  9354 

3697  9291 

3859  9225 

4019  9157 

4179  9085 

IS 

43 

3537  9353 

3700  9290 

3862  9224 

4022  9155 

4181  9084 

17 

44 

3540  9352 

3703  9289 

3864  9223 

4025  9154 

4184  9083 

16 

45 

3543  9351 

3706  9288 

3867  9222 

4027  9153 

4187  9081 

15 

46 

3546  9350 

3708  9287 

3870  9221 

4030  9152 

4189  9080 

14 

47 

3548  9349 

3711  9286 

3872  9220 

4033  9151 

4192  9079 

13 

48 

3551  9348 

3714  9285 

3875  9219 

4035  9150 

4195  9078 

12 

49 

3554  9347 

3716  9284 

3878  9218 

4038  9148 

4197  9077 

11 

50 

3557  9346 

3719  9283 

3881  9216 

4041  9147 

4200  9075 

lO 

51 

3559  9345 

3722  9282 

3883  9215 

4043  9146 

4202  9074 

9 

52 

3562  9344 

3724  9281 

3886  9214 

4046  9145 

4205  9073 

8 

S3 

3565  9343 

3727  9279 

3889  9213 

4049  9144 

4208  9072 

7 

54 

3567  9342 

3730  9278 

3891  9212 

4051  9143 

4210  9070 

6 

55 

3570  9341 

3733  9277 

3894  9211 

4054  9141 

4213  9069 

5 

56 

3573  9340 

3735  9276 

3897  9210 

4057  9140 

4216  9068 

4 

57 

3576  9339 

3738  9275 

3899  9208 

4059  9139 

4218  9067 

3 

58 

3578  9338 

3741  9274 

3902  9207 

4062  9138 

4221  9066 

2 

59 

3581  9337 

3743  9273 

3905  9206 

4065  9137 

4224  9064 

1 

60 

3584  9336 

3746  9272 

3907  9205 

4067  9135 

4226  9063 

O 

cos  sin 
69° 

COB  sin 
68° 

cos  sin 
67° 

cos  sin 
66° 

cos  sin 
65° 

.. 

1  ' 

'J 

25« 


26^ 


27^ 


28^ 


29° 


O 

1 
2 
3 
4 

5 

6 
7 
8 
9 

lO 

11 
12 
13 
14 

15 

16 
17 
18 
19 

20 

21 
22 
23 
24 

25 

26 
27 
28 
29 

30 

31 
32 
33 
34 

35 

36 
37 
38 
39 

40 

41 
42 
43 
44 

45 

46 
47 
48 
49 

50 

51 

52 
53 
54 

55 

56 
57 
58 
59 
60 


sin  cos 

4226  9063 

4229  9062 

4231  9061 

4234  9059 

4237  9058 

4239  9057 
4242  9056 
4245  9054 
4247  9053 
4250  9052 

4253  9051 
4255  9050 
4258  9048 
4260  9047 
4263  9046 

4266  9045 

4268  9043 

4271  9042 

4274  9041 

4276  9040 

4279  9038 

4281  9037 

4284  9036 

4287  9035 

4289  9033 

4292  9032 
4295  9031 
4297  9030 
4300  9028 
4302  9027 
4305  9026 
4308  9025 
4310  9023 
4313  9022 
4316  9021 
4318  9020 
4321  9018 
4323  9017 
4326  9016 
4329  9015 

4331  9013 
4334  9012 
4337  9011 
4339  9010 
4342  9008 


4344 
4347 
4350 
4352 
4355 
4358 
4360 
4363 
4365 
4368 

4371 
4373 
4376 
4378 
4381 

4384 
cos 


9007 
9006 
9004 
9003 
9002 

9001 
8999 
8998 
8997 
89% 
8994 
8993 
8992 
8990 
8989 

8988 
sin 


sin  cos 

4384  8988 

4386  8987 

4389  8985 

4392  8984 

4394  8983 


4397 
4399 
4402 
4405 
4407 

4410 
4412 
4415 
4418 
4420 

4423 
4425 
4428 
4431 
4433 
4436 
4439 
4441 
4444 
4446 

4449 
4452 
4454 
4457 
4459 
4462 
4465 
4467 
447P 
4472 

4475 
4478 
4480 
4483 
4485 
4488 
4491 
4493 
44% 
4498 

4501 
4504 
4506 
4509 
4511 
4514 
4517 
4519 
4522 
4524 

4527 
4530 
4532 
4535 
4537 
4540 
cos 


8982 
8980 
8979 
8978 
8976 

8975 
8974 
8973 
8971 
8970 

8%9 
8%7 
8966 
8%5 
8964 
8962 
8%1 
8960 
8958 
8957 

8956 
8955 
8953 
8952 
8951 
8949 
8948 
8947 
8945 
8944 

8943 
8942 
8940 
8939 
8938 

8936 
8935 
8934 
8932 
8931 

8930 
8928 
8927 
8926 
8925 
8923 
8922 
8921 
8919 
8918 

8917 
8915 
8914 
8913 
8911 
8910 
sin 


sin  cos 

4540  8910 

4542  8909 

4545  8907 

4548  8906 

4550  8905 

4553  8903 

4555  8902 

4558  8901 

4561  8899 

4563  8898 

4566  8897 
4568  8895 
4571  8894 
4574  8893 
4576  8892 

4579  8890 

4581  8889 

4584  8888 

4586  8886 

4589  8885 

4592  8884 

4594  8882 

4597  8881 

4599  8879 

4602  8878 

4605  8877 
4607  8875 
4610  8874 
4612  8873 
4615  8871 
4617  8870 
4620  8869 
4623  8867 
4625  8866 
4628  8865 
4630  8863 
4633  8862 
4636  8861 
4638  8859 
4641  $858 

4643  8857 
4646  8855 
4648  8854 
4651  8853 
4654  8851 


4656 
4659 
4661 
4664 
4666 

4669 
4672 
4674 
4677 
4679 

4682 
4684 
4687 
4690 
4692 

4695  8829 
cos  sin 


8850 
8849 
8847 
8846 
8844 

8843 
8842 
8840 
8839 
8838 
8836 
8835 
8834 
8832 
8831 


sin  cos 

4695  8829 

4697  8828 

4700  8827 

4702  8825 

4705  8824 

4708  8823 

4710  8821 

4713  8820 

4715  8819 

4718  8817 

4720  8816 
4723  8814 
4726  8813 
4728  8812 
4731  8810 
4733  8809 
4736  8808 
4738  8806 
4741  8805 
4743  8803 
4746  8802 
4749  8801 
4751  8799 
4754  8798 
4756  87% 

4759  8795 
4761  8794 
4764  8792 
4766  8791 
4769  8790 


4772 
4774 
4777 
4779 
4782 

4784 
4787 
4789 
4792 
4795 

4797 
4800 
4802 
4805 
4807 

4810 
4812 
4815 
4818 
4820 

4823 
4825 
4828 
4830 
4833 
4835 
4838 
4840 
4843 
4846 

4848 
cos 


8788 
8787 
8785 
8784 
8783 
8781 
8780 
8778 
8777 
8776 

8774 
8773 
8771 
8770 
8769 

8767 
8766 
8764 
8763 
8762 
8760 
8759 
8757 
8756 
8755 
8753 
8752 
8750 
8749 
8748 

8746 
sin 


64' 


63' 


62° 


ev 


sin  cos 

4848  8746 
4851  8745 
4853  8743 
4856  8742 
4858  8741 
4861  8739 
4863  8738 
4866  8736 
4868  8735 
4871  8733 
4874  8732 
4876  8731 
4879  8729 
4881  8728 
4884  8726 

4886  8725 
4889  8724  , 
4891  8722 
4894  8721 
48%  8719 

4899  8718 
4901  8716 
4904-8715 
4907  8714 
4909  8712 

4912  8711 
4914  8709 
4917  8708 
4919  870^ 
4922  8705 
4924  8704 
4927  8702 
4929  8701 
4932  8699 
4934  8698 

4937  86% 
y^   8695 
4942  8694 
49H  8692 
4947  8691 
4950  8689 
4952  8688 
4955  8686 
4957  8685 
4960  8683 
4%2  8682 
4%S  8681 
4%7  8679 
4970  8678 
4972  8676 
4975  8675 
4977  8673 
4980  8672 
4982  8670 
4985  8669 
4987  8668 
4990  8666 
4992  8665 
4995  8663 
4997  8662 

^QOO  8660 
\e<>s  sin' 

60° 


60 

59 
58 
57 
56 

55 

54 
S3 
52 
51 

50 

49 
48 
47 
46 

45 

44 
43 
42 
41 

40 

39 
38 
37 
36 

35 

34 
33 
32 
31 

30 

29 
28 
27 
26 

25 

24 
23 
22 
21 

20 

19 
IS 
17 
16 

15 

14 

13 

12 

11 

10 

9 

8 

7 

6 

5 

4 
3 
2 
1 


I 


L>i_ 


58 


NATURAL  SINES   AND   COSINES. 


30° 


31° 


32^ 


33*^ 


34° 


O 

1 
2 
3 

4 

5 

6 

7 
8 
9 

lO 

11 
12 
13 
14 

15 

16 
17 
18 
19 

20 

21 
22 
23 
24 

25 

26 
27 
28 
29 

30 

31 
32 
33 
34 

35 

36 
37 
38 
39 

40 

41 
42 
43 

44 

45 

46 
47 
48 
49 

50 

51 
52 
53 
54 

55 

56 

57 
58 
59 

60 


sin  cos 

5000  8660 

5003  8659 

5005  8657 

5008  8656 

5010  8654 

5013  8653 

5015  8652 

5018  8650 

5020  8649 

5023  8647 

5025  8646 
5028  8644 
5030  8643 
5033  8641 
5035  8640 

5038  8638 
5040  8637 
5043  8635 
5045  8634 
5048  8632 
^  5050  8631 
5053  8630 
5055  8628 
5058  8627 
5060  8625 
5063  8624 
5065  8622 
5068  8621 
5070  8619 
5073  8618 
5075  8616 
5078  8615 
5080  8613 
5083  8612 
5085  8610 
5088  8609 
5090  8607 
5093  8606 
5095  8604 
5098  8603 
5100  8601 
5103  8600 
5105  8599 
5108  8597 
5110  8596 
5113  8594 
5115  8593 
5118  8591 
5120  8590 
5123  8588 


5125 
5128 
5130 
5133 
5135 

5138 
5140 
5143 
5145 
5148 

5150 

COB 


8587 
8585 
8584 
8582 
8581 

8579 
8578 
8576 
8575 
8573 

8572 
sin 


sin  cos 

5150  8572 

5153  8570 

5155  8569 

5158  8567 

5160  8566 

5163  8564 

5165  8563 

5168  8561 

5170  8560 

5173  8558 

5175  8557 
5178  8555 
5180  8554 
5183  8552 
5185  8551 
5188  8549 
5190  8548 
5193  8546 
5195  8545 
5198  8543 
5200  8542 
5203  8540 
5205  8539 
5208  8537 
5210  8536 
5213  8534 
5215  8532 
5218  8531 
5220  8529 
5223  8528 
5225  8526 
5227  8525 
5230  8523 
5232  8522 
5235  8520 
5237  8519 
5240  8517 
5242  8516 
5245  8514 
5247  8513 

5250  8511 

5252  8510 

5255  8508 

5257  8507 

5260  8505 


69° 


5262 
5265 
5267 
5270 
5272 

5275 
5277 
5279 
5282 
5284 

5287 
5289 
5292 
5294 
5297 

5299 
cos 


58° 


sin  cos 

5299  8480 
5302  8479 
5304  8477 
5307  8476 
5309  8474 
5312  8473 
5314  8471 
5316  8470 
5319  8468 
5321  8467 

5324  8465 
5326  8463 
5329  8462 
5331  8460 
5334  8459 

5336  8457 
5339  8456 
5341  8454 
5344  8453 
5346  8451 
5348  8450 
5351  8448 
5353  8446 
5356  8445 
5358  8443 
5361  8442 
5363  8440 
5366  8439 
5368  8437 
5371  8435 
5373  8434 
5375  8432 
5378  8431 
5380  8429 
5383  8428 
5385  8426 
5388  8425 
5390  8423 
5393  8421 
5395  8420 
5398  8418 
5400  8417 
5402  8415 
5405  8414 
5407  8412 


8504 

8502 

8500* 

8499 

8497 

84% 
8494 
8493 
8491 
8490 

8488 
8487 
8485 
8484 
8482 

8480 
sin 


5410 
5412 
5415 
5417 
5420 

5422 
5424 
5427 
5429 
5432 
5434 
5437 
5439 
5442 
5444 

5446 
cos 


8410 
8409 
8407 
8406 
8404 

8403 
8401 
8399 
8398 
8396 

8395 
8393 
8391 
8390 
8388 

8387 
sin 


5T 


sin  cos 

5446  8387 
5449  8385 
5451  8384 
5454  8382 
5456  8380 
5459  8379 
5461  8377 
5463  8376 
5466  8374 
5468  8372 


5471 

8371 

5616 

5473 

8369 

5618 

5476 

8368 

5621 

5478 

8366 

5623 

5480 

8364 

5626 

5483  8363 
5485  8361 
5488  8360 
5490  8358 
5493  8356 
5495  8355 
5498  8353 
5500  8352 
5502  8350 
5505  8348 
5507  8347 
5510  8345 
5512  8344 
5515  8342 
5517  8340 


5519 
5522 
5524 
5527 
5529 

5531 
5534 
5536 
5539 
5541 


8339 
8337 
8336 
8334 
8332 

8331 
8329 
8328 
8326 
8324 


5544  8323 

5546  8321 

5548  8320 

5551  8318 

5553  8316 


5556 
5558 
5561 
5563 
5565 

5568 
5570 
5573 
5575 
5577 
5580 
5582 
5585 
5587 
5590 

5592 
cos 


8315 
8313 
8311 
8310 
8308 

8307 
8305 
8303 
8302 
8300 

8299 
8297 
8295 
8294 
8292 

8290 
sin 


56^ 


sin  cos 

5592  8290 
5594  8289 
5597  8287 
5599  8285 
5602  8284 
5604  8282 
5606  8281 
5609  8279 
5611  8?77 
5614  8276 
8274 
8272 
8271 
8269 
826a^ 

82^ 
8264 
8263 
8261 
8259 

8258 
8256 
8254 
8253 
8251 


5628 
5630 
5633 
5635 
5638 
5640 
5642 
5645 
5647 
5650 

5652  8249 
5654  8248 
5657  8246 
5659  8245 
5662  8243 

5664  8241 
5666  8240 
5669  8238 
5671  8236 
5674 
5676  8233 
5678  8231 
5681  8230 
5683  8228 
5686  8226 
5688  8225 
5690  8223 
5693  8221 
5695  8220 
5698  8218 
5700  8216 
5702  8215 
5705  8213 
5707  8211 
5710  8210 

5712  8208 
5714  8207 
5717  8205 
5719  8203 
5721  8202 

5724  8200 

5726  8198 

5729  8197 

5731  8195 

5733  8193 

5736  8192 

cos  sin 


55° 


60 

59 
58 
57 
56 

55 

54 
53 
52 
51 

50 

49 
48 
47 
46 

45 

44 
43 
42 
41 

40 

39 
38 
37 
36 

36 

34 
33 
32 
31 

30 

29 
28 
27 
26 

25 

24 
23 
22 
21 
20 
19 
18 
17 
16 

16 

14 
13 
12 
11 

10 

9 
8 
7 
6 

5 

4 
3 
2 
1 

O 


NATURAL  SINES  AND  COSINES. 


O 

1 
2 
3 
4 

5 

6 

7 

8 

.9 

10 

11 
12 
13 
14 

15 

16 
17 
18 
19 

20 

21 
22 
23 
24 

26 

26 
27 
28 
29 

30 

31 
32 
33 
34. 

36 

36 
37 
38 
39 

40 

41 
42 
43 
44 

46 

46 
47 
48 
49 

1? 

52 
53 
54 

66 

56 

57 
58 
59 

60 


59 


35° 


36^^ 


37* 


38^ 


39° 


sin  cos 

5736  8192 

5738  8190 

5741  8188 

5743  8187 

5745  8185 

5748  8183 

5750  8181 

5752  8180 

5755  8178 

5757  8176 

5760  8175 

5762  8173 

5764  8171 

5767  8170 

5769  8168 

5771  8166 

5774  8165 

5776  8163 

5779  8161 

5781  8160 

5783  8158 

5786  8156 

5788  8155 

5790  8153 

5793  8151 

5795  8150 

5798  8148 

5800  8146 

5802  8145 

5805  8143 


5807 
5809 
5812 
5814 
5816 

5819 
5821 

5824 
5826 
5828 

5831 
5833 
5835 
5838 
5840 

5842 
5845 
5847 
5850 
5852 

5854 
5857 
5859 
5861 
5864 

5866 
5868 
5871 
5873 
5875 

5878 
cos 


8141 
8139 
8138 
8136 
8134 

8133 
8131 
8129 
8128 
8126 
8124 
8123 
8121 
8119 
8117 

8116 
8114 
8112 
8111 
8109 

8107 
8106 
8104 
8102 
8100 

8099 
8097 
8095 
8094 
8092 
8090 
sin 


54^ 


sin  cos 

5878  8090 

5880  8088 

5883  8087 

5885  8085 

5887  8083 

5890  8082 

5892  8080 

5894  8078 

5897  8076 

5899  8075 

5901  8073 
5904  8071 
5906  8070 
5908  8068 
5911  8066 
5913  8064 
5915  8063 
5918  8061 
5920  8059 
5922  8058 

5925  8056 

5927  8054 

5930  8052 

5932  8051 

5934  8049 

5937  8047 
5939  8045 
5941  8044 
5944  8042 
5946  8040 

5948  8039 
5951' 8D37 
5953  8035 
5955  8033 
5958  8032 

5960  8039 

5%2  8028 

5965  8026 

5%7  8025 

5%9  8023 

5972  8021 

5974  8020 

5976  8018 

5979  8016 

5981  8014 


5983 
5986 
5988 
5990 
5993 

5995 
5997 

60^ 
6004 

6007 
6009 
6011 
6014 
6016 

6018 
cos 


8013 
8011 
8009 
8007 
8006 

8004 
8002 
8000 
7999 
7997 
7995 
7993 
7992 
7990 
7988 

7986. 
sin 


63^ 


sin 

6018 
6020 
6023 
6025 
6027 
6030 
6032 
6034 
6037 
6039 

6041 
60H 
6046 
6048 
6051 
6053 
6055 
6058 
6060 
6062 

6065 
6067 
6069 
6071 
6074 

6076 
6078 
6081 
6083 
6085 

6088 
6090 
6092 
6095 
6097 

6099 
6101 
6104 
6106 
6108 

6111 
6113 
6115 
6118 
6120 

6122 
6124 
6127 
6129 
6131 

6134 
6136 
6138 
6141 
6143 
6145 
6147 
6150 
6152 
6154 

'i^ 
Si 


cos 

7986 
7985 
7983 
7981 
7979 
7978 
7976 
7974 
7972 
7971 

7%9 
7%7 
7%5 
7964 
7962 

7960 
7958 
7956 
7955 
7953 

7951 
7950 
7948 
7946 
7944 

7942 
7941 
7939 
7937 
7935 

7934 
7932 
7930 
7928 
7926 

7925 
7923 
7921 
7919 
7918 
7916 
7914 
7912 
7910 
7909 

7907 
7905 
7903 
7902 
7900 

7898 
78% 
7894 
7893 
789f 
7889 
7b37 
7885 
7884 
7882 

7880 
sin 


52' 


sin  cos 

6157  7880 
6159  7878 
616U7877 
6163  .7875 
6166  7873 
6168  7871 
6170  7869 
6173  7868 
6175  7866 
6177  7864 


6180 
6182 
6184 
6186 
6189 

6191 
6193 
61% 
6198 
6200 


7862 
7860 
7859 
7857 
7855 

7853 
7851 
7850 
7848 
7346 


6202  7844 

6205  7842 

6207  7841 

6209  7839 

6211  7837 


6214 
6216 
6218 
6221 
6223 

6225 
6227 
6230 
6232 
6234 

6237 
6239 
6241 
6243 
6246 
6248  7808 
6250  7806 
6252  7804 
6255  7802 
6257  7801 


7835 
7833 
7832 
7830 
7828 

7826 
7824 
7822 
7821 
7819 

7817 
7815 
7813 
7812 
7810 


6259 
6262 
6264 
6266 
6268 

6271 
6273 
6275 
6277 
6280 

6282 
6284 
6286 
6289 
6291 


7799 
7797 
7795 
7793 
7792 

7790 
7788 
7786 
7784 
7782 

7781 
7779 
•7777 
7775 
7773 


6293  7771, 
cos  sin 


sin  cos 

6293  7771 

6295  7770 

6298  7768 

6300  7766 

6302  7764 

6305  7762 

6307  7760 

6309  7759 

6311  7757 

6314  7755 

6316  7753 

6318  7751 

6320  7749 

6323  7748 

6325  7746 

6327  7744 

6329  7742 

6332  7740 

6334  7738 

6336  7V37 

6338  7735 
6341  7733 
6343  7731 
6345  7729 
6347  7727 
7725 
7724 
7722 
7720 
7718 


6350 
6352 
6354 
6356 
6359 

6361 
6363 
6365 
6368 
6370 

6372 
6374 
9376 
6379 
6381 
6383 
6385 
6388 
6390 
6392 

6394 
6397 
6399 
6401 
6403 

6406 
6408 
6410 
6412 
6414 

6417 
6419 
'6421 
6423 
6426 

6428 

COM 


7716 
7714 
7713 
7711 
7709 

7707 
7705 
7703 
7701 
7700 
7698 
76% 
7694 
7692 
7690 

7688 
7687 
7685 
7683 
7681 

7679 
7677 
7675 
7674 
7672 

7670 
7668 
7666 
7664 
7662 

7660 
sin 


61* 


60^ 


60 

59 
58 
57 
56 

56 

54 
S3 
52 
51 

60 

49 
48 
47 
46 

46 

44 
43 
42 
41 

40 

39 

38 
37 
36. 

35 

34 
33 
32 
31 

30 

29 
28 
27 
26 

26 

24 
23 
22 
21- 

26 

19 
18 
17 
16, 

16 

14 
13 
12 
11 

10 

9 

6 

6 

4 
3 
2 
1 

O 


4. 


1  • 


y 


MM 


\ 


m 


NATURAL  SINES  AND  COSINES. 


NATURAL  TANGENTS  AND  COTANGENTS. 


61 


40° 


41^ 


42' 


43' 


44° 


O 

1 
2 
3 

4 

5 

6 

7 
8 
9 

10 

11 
12 
13 
14 

15 

16 
17 
18 
19 

20 

21 
22 
23 
24 

25 

26 
27 
28 
29 

ao 

31 
32 
33 
34 

35 

36 
37 
38 
39 

40 

41 
42 
43 
44 

45 

46 
47 
48 
49 

50 

51 
52 
53 
54 

55 

56 

57 
58 
59 

60 


sin   cos 

6428  7660 
6430  7659 
6432  7657 
6435  7655 
6437  7653 
6439  7651 
6441  7649 
6443  7647 
6446  7645 
6448  7644 
6450  7642 
6452  7640 
6455  7638 
6457  7636 
6459  7634 
6461  7632 
6463  7630 
6466  7629 
6468  7627 
6470  7625 

6472 

6475 

6477 

6479 

6481 

6483 

6486 

6488 

6490 

6492 


sin 

6561 
6563 
6565 
6567 
6569 
6572 
6574 
6576 
6578 
6580 


cos 

7547 
7545 
7543 
7541 
7539 

7538 
7536 
7534 
7532 
7530 


7623 
7621 
7619 
7617 
7615 

7613 
7612 
7610 
7606 
7606 

6494  7604 
6497  7602 
6499  7600 
6501  7598 
6503  7596 
6506  7595 
6508  7593 
6510  7591 
6512  7589 
6514  7587 
6517  7585 
6519  7583 
6521  758L 
6523  7579 
6525  7578 


6583  7528 
6585  7526 
6587  7524 
6589  7522 
6591  7520 
6593  7518 
6596  7516 
6598  7515 
6600  7513 
6602  7511 

6604  7509 
6607  7507 
6609  7505 
6611  7503 
6613  7501 
6615  7499 
6617  7497 
6620  7495 
6622  7493 
6624  7491 
6626  7490 
6628  7488 
6631  7486 
6633  7484 
6635  7482 
6637  7480 
6639  7478 
6641  7476 
6644  7474 
6646  7472 

6648  7470 

6650  7468 

6652  7466 

6654  7464 

6657  7463 


sin  cos 

6691  7431 

6693  7430 

6696  7428 

6698  7426 

6700  7424 

6702  7422 

6704  7420 

6706  7418 

6709  7416 

6711  7414 

6713  7412 

6715  7410 

6717  7408 

6719  7406 

6722  7404 

6724  7402 

6726  7400 

6728  7398 

6730  73% 

6732  7394 

6734  7392 

6737  7390 

6739  7388 

6741  7387 

6743  7385 

6745  7383 
6747  7381 
6749  7379 
6752  7377 
6754  7375 
6756  7373 
6758  7371 
6760  7369 
6762  7367 
6764  7365 
6767  7363 
6769  7361 
6771  7359 
6773  7357 
6775  7355 

6777  7253 

6779  7351 

6782  7349 

6784  7347 

6786  7345 


sin 

6820 
6822 
6824 
6826 
6828 

6831 
6833 
6835 
6837 
6839 


cos 

7314 
7312 
7310 
7308 
7306 

7304 
7302 
7300 
7298 
7296 


6841  7294 
6843  7292 
6845  7290 
6848  7288 
6850  7286 
6852  7284 
6854  7282 
6856  7280 
6858  7278 
6860  7276 
6862  7274 
68fe5  7272 
6867  7270 
6869  7268 
6871  7266 
6873  7264 
6875  7262 
6877  7260 
6879  7258 
6881  7256 

6884  7254 
6886  7252 
6888  7250 
6890  7248 
6892  7246 

6894  7244 
68%  7242 
6898  7240 
6900  7238 
6903  7236 
6905  7234 
6907  7232 
6909  7230 
6911  7228 
6913  7226 


6528 
6530 
6532 
6534 
6536 

6539 
6541 
6543 
6545 
6547 

6550 
6552 
6554 
6556 
6558 

6561 
cos 


7576 
7574 
7572 
7570 
7568 

7566 
7564 
7562 
7560 
7559 

7557 
7555 
7553 
7551 
7549 

7547 
sin 


6659 
6661 
6663 
6665 
6667 

6670 
6672 
6674 
6676 
6678 

6680 
6683 
6685 
6687 
6689 

6691 
.  cos 


7461 
7459 
7457 
7455 
7453 

7451 
7449 
7447 
7445 
7443 
7441 
7439 
7437 
743i) 
7433 

7431 
sin 


7343 
7341 
7339 
7337 
7335 
7333 
7331 
7329 
7327 
7325 

7323 
7321 
7319 
7318 
7316 

7.n4 

cos   Si"l 


6788 

6790 

6792 

6794 

6797 

6799 

6801 

6803 

6805 

6807 

6809 

6SV. 

6814 

6816 

6818 

6820 


6915 
6917 
6919 
6921 
6924 

6926 
6928 
6930 
6932 
6934 
6936 
6938 
6940 
6942 
6944 

6947 
cos 


7224 
7222 
7220 
7218 
7216 

7214 
7212 
7210 
7208 
7206 

7203 
7201 
7199 
7197 
7195 
7193 
sin 


sin  cos 

6947  7193 

6949  7191 

6951  7189 

6953  7187 

6955  7185 

6957  7183 
6959  7181 
6%1  7179 
6963  7177 
6%5  7175 

6%7  7173 

6970  7171 

6972  7169 

6974  7167 

6976  7165 

6978  7163 

6980  7161 

6982  7159 

6984  7157 

6986  7155 

6988  7153 

6990  7151 

6992  7149 

6995  7147 

6997  7145 

6999  7143 
7001  7141 
7003  7139 
7005  7137 
7007  7135 
7009  7133 
7011  7130 
7013  7128 
7015  7126 
7017  7124 
7019  7122 
7022  7120 
7024  7118 
7026  7116 
7028  7114 

7030  7112 
7032  7110 
7034  7108 
7036  7106 
7038  7104 
7040  7102 
7042  7100 
7044  7098 
7046  70% 
7048  7094 
7050  7092 
7053  7090 
7055  7088 
7057  7085 
7059  7083 

7061  7081 

7063  7079 

7065  7077 

7067  7075 

7069  7073 

■^   707i"-VD71 
•  cos^'tlrf: 


40° 


48' 


47' 


46' 


45 


60 

59 
58 
57 
56 

55 

54 
53 
52 
51 

50 

49 
48 
47 
46 

45 

44 
43 
42 
41 

40 

39 
38 
37 
36 

35 

34 
33 
32 
31 

30 

29 
28 
27 
26 

25 

.24 
23 
22 
21 

20 

19 
18 
17 
16 

15 

14 
13 
12 
11 

10 

9 
8 
7 
6 

5 

4 
3 
2 
1 
O 


o 

1 

2 
3 
4 

5 

6 
7 
8 
9 

10 

11 
12 
13 
14 

15 

16 
17 
18 
19 

20 

21 
22 
23 
24 

25 

26 
27 
28 
29 

30 

31 
32 
33 
34 

35 

36 
37 
38 
39 

40 

41 
42 
43 
44 

45 

46 
47 
48 
49 

50 

51 
52 
53 
54 

55 

56 
57 
58 
59 
60 


O' 


2° 


3° 


tan 

0000 
0003 
0006 
0009 
0012 

0015 
0017 
0020 
0023 
0026 

0029 
0032 
0035 
0038 
0041 
0044 
0047 
0049 
0052 
0055 

0058 
0061 
0064 
0067 
0070 

0073 
0076 
0079 
0081 
0084 

0087 
0090 
0093 
00% 
0099 
0102 
0105 
0108 
0111 
0113 

0116 
0119 
0122 
0125 
0128 

0131 
0134 
0137 
0140 
0143 
0146 
0148 
0151 
0154 
0157 
0160 
0163 
0166 
0169 
0172 
0175 
cot 


cot 

Infinite 
3437.75 
1718.87 
1145.92 
859.436 
687.549 
572.957 
491.106 
429.718 
381.971 
343.774 
312.521 
286.478 
264.441 
245.552 
229.182 
214.858 
202.219 
190.984 
180.932 

171.885 
163.700 
156.259 
149.465 
143.237 
137.507 
132.219 
127.321 
122.774 
118.540 

114.589 
110.892 
107.426 
104.171 
101.107 
98.2179 
95.4895 
92.9085 
90.4633 
88.1436 
85.9398 
83.8435 
81.8470 
79.9434 
78.1263 

76.3900 
74.7292 
73.1390 
71.6151 
70.1533 

68.7501 
67.4019 
66.1055 
64.8580 
63.6567 
62.4992 
61.3829 
60.3058 
59.2659 
58.2612 

57.2900 
ton 


tan 

0175 
0177 
0180 
0183 
0186 

0189 
0192 
0195 
0198 
0201 

0204 
0207 
0209 
0212 
0215 
0218 
0221 
0224 
0227 
0230 

0233 
0236 
0239 
0241 
0244 
0247 
0250 
0253 
0256 
0259 

0262 
0265 
0268 
0271 
0274 

0276 
0279 
0282 
0285 
0288 

0291 
0294 
0297 
0300 
0303 

0306 
0308 
0311 
0314 
0317 
0320 
0323 
0326 
0329 
0332 

0335 
0338 
0340 
0343 
0346 

0349 
cot 


cot 

57.2900 
56.3506 
55.4415 
54.5613 
53.7086 
52.8821 
52.0807 
51.3032 
50.5485 
49.8157 

49.1039 
48.4121 
47.7395 
47.0853 
46.4489 
45.8294 
45.2261 
44.6386 
44.0661 
43.5081 

42.9641 
42.4335 
41.9158 
41.4106 
40.9174 
40.4358 
39.%55 
39.5059 
39.0568 
38.6177' 

38.1885 
37.7686 
37.3579 
36.9560 
36.5627 

36.1776 
35.8006 
35.4313 
35.0695 
34.7151 

34.3678 
34.0273 
33.6935 
33.3662 
33.0452 

32.7303 
32.4213 
32.1181 
31.8205 
31.5284 
31.2416 
30.9599 
30.6833 
30.4116 
30.1446 

29.8823 
29.6245 
29.3711 
29.1220 
28.8771 
28.6363 
tan 


tan 

0349 
0352 
0355 
0358 
0361 

0364 
0367 
0370 
0373 
0375 

0378 
0381 
0384 
0387 
0390 
0393 
03% 
0399 
0402 
0405 


cot 

28.6363 
28.3994 
28.1664 
27.9372 
27.7117 
27.4899 
27.2715 
27.0566 
26.8450 
26.6367 

26.4316 
26.22% 
26.0307 
25.8348 
25.641.8 

25.4517 
25.2644 
25.0798 
24.8978 
24.7185 


0407  24.5418 
0410  24.3675 
0413  24.1957 
0416  24.0263 
0419.^.8593 
0422  23.6945 
23.5321 
23.3718 
23.2137 
23.0577 

22.9038 
22.7519 
22.6020 
22.4541 
22J081 


0442 
0445 
0448 

0451 
0454 
0457 
0460 
0463 
0466 
0469 
0472 
0475 
0477 
0480 
0483 
0486 
0489 
0492 

0495 
0498 
0501 
0504 
0507 

0509 
0512 
0515 
0518 
0521 
0524 
cot 


22.1640 
22.0217 
21.8813 
21.7426 
21.6056 
21.4704 
21.3369 
21.2049 
21.0747 
20.9460 

20.8188 
20.6932 
20.5691 
20.4465 
20.3253 

20.2056 
20.0872 
19.9702 
19.8546 
19.7403 

19.6273 
19.5156 
19.4051 
19.2959 
19.1879 

19.0811 
tan 


tan 

0524 
0527 
0530 
0533 
0536 

0539 
0542 
0544 
0547 
0550 

0553 
0556 
0559 
0562 
0565 
0568 
0571 
0574 
0577 
0580 

0582 
0585 
0588 
0591 
0594 

0597 
0600 
0603 
0606 
0609 
0612 
0615 
0617 
0620 
0623 

0626 
0629 
0632 
0635 
0638 
0641 
0644 
0647 
0650 
0653 

0655 
0658 
0661 
0664 
0667 
0670 
0673 
0676 
0679 
0682 

0685 
0688 
0690 
0693 
06% 

0699 
cot 


cot 

19.0811 
18.9755 
18.8711 
18.7678 
18.6656 

18.5645 
18.4645 
18.3655 
18.2677 
18.1708 

18.0750 
17.9802 
17.8863 
17.7934 
17.7015 
17.6106 
17.5205 
17.4314 
17.3432 
17.2558 
17.1693 
17.0837 
16.9990 
16.9150 
16.8319 
16.74% 
16.6681 
16.5874 
.16.5075 
16.4283 

16.3499 
16.2722 
16.1952 
16.1190 
16.0435 

15.9687 
15.8945 
15.8211 
15.7483 
15.6762 

15.6048 
15.5340 
15.4638 
15.3943 
15.3254 

15.2571 
15.1893 
15.1222 
15.0557 
14.9898 

14.9244 
14.85% 
14.7954 
14.7317 
14.6685 

14.6059 
14.5438 
14.4823 
14.4212 
143607 
14.3007 
tan 


tan 

0699 
0702 
0705 
0708 
0711 
0714 
0717 
0720 
0723 
0726 

0729 
0731 
0734 
0737 
0740 

0743 
0746 
0749 
0752 
0755 

0758 
0761 
0764 
0767 
0769 

0772 
0775 
0778 
0781 
0784 

0787 
0790 
07^3 
07% 
0799 
0802 
0805 
0808 
0810 
0813 
0816 
0819 
0822 
0825 
0828 

0831 
0834 
0837 
0840 
0843 

0846 
0849 
0851 
0854 
0857 

0860 

0863. 

0866 

0869 

0872 

0875 
cot 


cot 

143007 
14.2411 
14.1821 
14.1235 
14.0655 

14.0079 
13.9507 
13.8940 
13.8378 
13.7821 

13.7267 
13.6719 
13.6174 
13.5634 
13.5098 
13.4566 
13.4039 
13.3515 
13.29% 
13.2480 

13.1969 
13.1461 
13.0958 
13.0458 
12.9%2 

12.9469 
12.8981 
12.84% 
12.8014 
12.7536 
12.7062 
12.6591 
12.6124 
12.5660 
12.5.199 
12.4742 
12.4288 
12.3838 
12.3390 
12.2946 
12.2505 
12.2067 
12.1632 
12.1201 
12.0772 

12.0346 
11.9923 
11.9504 
11.9087 
11.8673 
11.8262 
11.7853 
11.7448 
11.7045 
11.6645 

11.6248 
11.5853 
11.5461 
11.5072 
11.4685 

11.4301 
tan 


89' 


88' 


87' 


86' 


85< 


60 

59 

58 
57 
56 

55 

54 
53 
52 
51 

50 

49 
48 
47 
46 

45 

44 
43 
42 
41 

40 

39 
38 
37 
36 

35 

34 
33 
32 
31 

30 

29 
28 
27 
26 

25 

24 
23 
22 
21 

20 

19 
18 
17 
16 

15 

14 
13 
12 
11 

10 

9 

8 
7 
6 

5 

4 
3 
2 
1 

O 


62 


NATURAL  TANGENTS   AND   COTANGENTS. 


I 


111 


f 

5P 

ep 

70 

8° 

9° 

f 

tan   cot 

tan  cot 

tan   cot 

tan   cot 

tan   cot 

o 

0875  11.4301 

1051  9.5144 

1228  8.1443 

1405  7.1154 

1584  6.3138 

60 

1 

0878  11.3919 

1054  9.4878 

1231  8.1248 

1408  7.1004 

1587  6.3019 

59 

2 

0881  11.3540 

1057  9.4614 

1234  8.1054 

1411  7.0855 

1590  6.2901 

58 

3 

0884  11.3163 

1060  9.4352 

1237  8.0860 

1414  7.0706 

1593  6.2783 

57 

4 

0887  11.2789 

1063  9.4090 

1240  8.0667 

1417  7.0558 

15%  6.2666 

56 

5 

0890  11.2417 

1066  9.3831 

1243  8.0476 

1420  7.0410 

1599  6.2549 

55 

6 

0892  11.2048 

1069  9.3572 

1246  8.0285 

1423  7.0264 

1602  6.2432 

54 

7 

0895  11.1681 

1072  9.3315 

1249  8.0095 

1426  7.0117 

1605  6.2316 

53 

8 

0898  11.1316 

1075  9.3060 

1251  7.9906 

1429  6.9972 

1608  6.2200 

52 

9 

0901  11.0954 

1078  9.2806 

1254  7.9718 

1432  6.9827 

1611  6.2085 

51 

lO 

0901  11.0594 

1080  9.2553 

1257  7.9530 

1435  6.9682 

1614  6.1970 

50 

11 

0907  11.0237 

1083  9.2302 

1260  7.9344 

1438  6.9538 

1617  6.1856 

49 

12 

0910  10.9882 

1086  9.2052 

1263  7.9158 

1441  6.9395 

1620  6.1742 

48 

13 

0913  10.9529 

1089  9.1803 

1266  7.8973 

1444  6.9252 

1623  6.1628 

47 

14 

0916  10.9178 

1092  9.1555 

1269  7.8789 

1447  6.9110 

1626  6.1515 

46 

16 

0919  10.8829 

1095  9.1309 

1272  7.8606 

1450  6.8%9 

1629  6.1402 

45 

16 

0922  10.8483 

1098  9.1065 

1275  7.8424 

1453  6.8828 

1632  6.1290 

44 

17 

0925  10.8139 

1101  9.0821 

1278  7.8243 

1456  6.8687 

1635  6.1178 

43 

18 

0928  10.7797 

1104  9.0579 

1281  7.8062 

1459  6.8548 

1638  6.1066 

42 

19 

0931  10.7457 

1107  9.0338 

1284  7.7883 

1462  6.8408 

1641  6.0955 

41 

20 

0934  10.7119 

1110  9.0098 

1287  7.7704 

1465  6.8269 

1644  6.0844 

40 

21 

0936  10.6783 

1113  8.9860 

1290  7.7525 

1468  6.8131 

1647  6.0734 

39 

22 

0939  10.6450 

1116  8.%23 

1293  7.7348 

1471  6.7994 

1650  6.0624 

38 

23 

0942  10.6118 

1119  8.9387 

12%  7.7171 

1474  6.7856 

1653  6.0514 

37 

24 

0945  10.5789 

1122  8.9152 

1299  7.69% 

1477  6.7720 

1655  6.0405 

36 

25 

0948  10.5462 

1125  8.8919 

1302  7.6821 

1480  6.7584 

1658  6.02% 

35 

26 

0951  10.5136 

1128  8.8686 

1305  7.6647 

1483  6.7448 

1661  6.0188 

34 

27 

0954  10.4813 

1131  8.8455 

1308  7.6473 

1486  6.7313 

1664  6.0080 

33 

28 

0957  10.4491 

1134  8.8225 

1311  7.6301 

1489  6.7179 

1667  5.9972 

32 

29 

0960  10.4172 

1136  8.7996 

1314  7.6129 

1492  6.7045 

1670  5.9865 

31 

30 

0%3  10.3854 

1139  8.7769 

1317  7.5958 

1495  6.6912 

1673  5.9758 

30 

31 

0966  10.3538 

1142  8.7542 

1319  7.5787 

1497  6.6779 

1676  5.%51 

29 

32 

0%9  10.3224 

1145  8.7317 

1322  7.5618 

1500  6.6646 

1679  5.9545 

28 

33 

0972  10.2913 

1148  8.7093 

1325  7.5449 

1503  6.6514 

1682  5.9439 

27 

34 

0975  10.2602 

1151  8.6870 

1328  7.5281 

1506  6.6383 

1685  5.9333 

26 

35 

0978  10.2294 

1154  8.6648 

1331  7.5113 

1509  6.6252 

1688  5.9228 

25 

36 

0981  10.1988 

1157  8.6427 

1334  7.4947 

1512  6.6122 

1691  5.9124 

24 

37 

0983  10.1683 

1160  8.6208 

1337  7.4781 

1515  6.5992 

1694  5.9019 

23 

38 

0986  10.1381 

1163  8.5989 

1340  7.4615 

1518  6.5863 

1697  5.8915 

22 

39 

0989  10.1080 

1166  8.5772 

1343  7.4451 

1521  6.5734 

1700  5.8811 

21 

40 

0992  10.0780 

1169  8.5555 

1346  7.4287 

1524  6.5606 

1703  5.8708 

20 

41 

0995  10.(H83 

1172  8.5340 

1349  7.4124 

1527  6.5478 

1706  5.8605 

19 

42 

0998  10.0187 

1175  8.5126 

1352  7.3%2 

1530  6.5350 

1709  5.8502 

18 

43 

1001  9.9893 

1178  8.4913 

1355  7.3800 

1533  6.5223 

1712  5.8400 

17 

44 

1004  9.9601 

1181  8.4701 

1358  7.3639 

1536  6.5097 

1715  5.8298 

16 

45 

1007  9.9310 

1184  8.4490 

1361  7.3479 

1539  6.4971 

1718  5.8197 

15 

46 

1010  9.9021 

1187  8.4280 

1364  7.3319 

1542  6.4846 

1721  5.8095 

14 

47 

1013  9.8734 

1189  8.4071 

1367  7.3160 

1545  6.4721 

1724  5.7994 

13 

48 

1016  9.8448 

1192  8.3863 

1370  7.3002 

1548  6.45% 

J727  5.7894 

12 

49 

1019  9.8164 

1195  8.3656 

1373  7.2844 

1551  6.4472 

1730  5.7794 

11 

50 

1022  9.7882 

1198  8.3450 

1376  7.2687 

1554  6.4348 

1733  5.7694 

10 

51 

1025  9.7601 

1201  8.3245 

1379  7.2531 

1557  6.4225 

1736  5.7594 

9 

52 

1028  9.7322 

1204  8.3041 

1382  7.2375 

1560  6.4103 

1739  5.7495 

8 

53 

1030  9.70H 

1207  8.2838 

1385  7.2220 

1563  6.3980 

1742  5.73% 

7 

54 

1033  9.6768 

1210  8.2636 

1388  7.2066 

1566  6.3859 

1745  5.7297 

6 

55 

1036  9.6499 

1213  8.2434 

1391  7.1912 

1569  6.3737 

1748  5.7199 

5 

56 

1039  9.6220 

1216  8.2234 

1394  7.1759 

1572  6.3617 

1751  5.7101 

4 

57 

1042  9.59*9 

1219  8.2035 

1397  7.1607 

1575  6.34% 

1754  5.7004 

3 

58 

1045  9.5679 

1222  8.1837 

1399  7.1455 

1578  6.3376 

1757  5.6906 

2 

59 

1048  9.5411 

1225  8.1640 

1402  7.1304 

1581  6.3257 

1760  5.6809 

1 

eo 

1051  9.5144 

1228  8.1443 

1405  7.1154 

1584  6.3138 

1763  5.6713 

0 

cot   tan 
84° 

cot  tan 
83° 

cot   tan 
82° 

cot   tan 
81° 

cot   tan 
80° 

/ 

f 

NATURAL  TANGENTS  AND 

COTANGENTS. 

biS 

f 

10° 

11° 

12° 

13° 

14° 

f 

tan  cot 

tan 

cot 

tan 

cot 

tan 

cot 

tan 

cot 

0 

1763  5.6713 

1944 

5.1446 

2126 

4.7046 

2309 

4.3315 

2493 

4.0108 

60 

1 

1766  5.6617 

1947 

5.1366 

2129 

4.6979 

2312 

4.3257 

24% 

4.0058 

59 

2 

1769  5.6521 

1950 

5.1286 

2132 

4.6912 

2315 

4.3200 

2499 

4.0009 

58 

3 

1772  5.6425 

1953 

5.1207 

2135 

4.6845 

2318 

4.3143 

2503 

3.9959 

57 

4 

1775  5.6330 

1956 

5.1128 

2138 

4.6779 

2321 

4.3086 

2506 

3.9910 

56 

5 

1778  5.6234 

1959 

5.1049 

2141 

4.6712 

2324 

4.3029 

2509 

3.9861 

55 

6 

1781  5.6140 

1%2 

5.0970 

2144 

4.6646 

2327 

4.2972 

2512 

3.9812 

54 

7 

1784  5.6045 

1965 

5.0892 

2147 

4.6580 

2330 

4.2916 

2515 

3.9763 

53 

8 

1787  5.5951 

1968 

5.0814 

2150 

4.6514 

2333 

4.2859 

2518 

3.9714 

52 

9 

1790  5.5857 

1971 

5.0736 

2153 

4.6448 

2336 

4.2803 

2521 

3.9665 

51 

10 

1793  5.5764 

1974 

5.0658 

2156 

4.6382 

2339 

4.2747 

2524 

3.%17 

50 

11 

17%  5.5671 

1977 

5.0581 

2159 

4.6317 

2342 

4.2691 

2527 

3.9568 

49 

12 

1799  5.5578 

1980 

5.0504 

2162 

4.6252 

2345 

4.2635 

2530 

3.9520 

48 

13 

1802  5.5485 

1983 

5.0427 

2165 

4.6187 

2349 

4.2580 

2533 

3.9471 

47 

14 

1805  5.5393 

1986 

5.0350 

2168 

4.6122 

2352 

4.2524 

2537 

3.9423 

46 

15 

1808  5.5301 

1989 

5.0273 

2171 

4.6057 

2355 

4.2468 

2540 

3.9375 

45 

16 

1811  5.5209 

1992 

5.0197 

2174 

4.5993 

2358 

4.2413 

2543 

3.9327 

44 

17 

1814  5.5118 

1995 

5.0121 

2177 

4.5928 

2361 

4.2358 

2546 

3.9279 

43 

18 

1817  5.5026 

1998 

5.0045 

2180 

4.5864 

2364 

4.2303 

2549 

3.9232 

42 

19 

1820  5.4936 

2001 

4.9969 

2183 

4.5800 

2367 

4.2248 

2552 

3.9184 

41 

20 

1823  5.4845 

2004 

4.9894 

2186 

4.5736 

2370 

4.2193 

2555 

3.9136 

40 

21 

1826  5.4755 

2007 

4.9819 

2189 

4.5673 

2373 

4.2139 

2558 

3.9089 

39 

22 

1829  5.4665 

2010 

4.9744 

2193 

4.5609 

2376 

4.2084 

2561 

3.9042 

Z^ 

23 

1832  5.4575 

2013 

4.9669 

21% 

4.5546 

2379 

4.2030 

2564 

3.8995 

37 

24 

1835  5.4486 

2016 

4.9594 

2199 

4.5483 

2382 

4.1976 

2568 

3.8947 

36 

25 

1838  5.4397 

2019 

4.9520 

2202 

4.5420 

2385 

4.1922 

2571 

3.8900 

35 

26 

1841  5.4303 

2022 

4.9446 

2205 

4.5357 

2388 

4.1868 

2574 

3.8854 

34 

27 

1844  5.4219 

2025 

4.9372 

2208 

4.5294 

2392 

4.1814 

2577 

3.8807 

33 

28 

1847  5.4131 

2028 

4.9298 

2211 

4.5232 

2395 

4.1760 

2580 

3.8760 

32 

29 

1850  5.4043 

2031 

4.9225 

2214 

4.5169 

2398 

4.1706 

2583 

3.8714 

31 

30 

1853  5.3955 

2035 

4.9152 

2217 

4.5107 

2401 

4.1653 

2586 

3.8667 

30 

31 

1856  5.3868 

2038 

4.9078 

2220 

4.5045 

2404 

4.1600 

2589 

3.8621 

29 

32 

1859  5.3781 

2941 

4.9006 

2223 

4.4983 

2407 

4.1547 

2592 

3.8575 

28 

33 

1862  5.3694 

2044 

4.8933 

2226 

4.4922 

2410 

4.1493 

2595 

3.8528 

27 

34 

1865  5.3607 

2047 

4.8860 

2229 

4.4860 

2413 

4.1441 

2599 

3.8482 

26 

35 

1868  5.3521 

2050 

4.8788 

2232 

4.4799 

2416 

4.1388 

2602 

3.8436 

25 

36 

1871  5.3435 

2053 

4.8716 

2235 

4.4737 

2419 

4.1335 

2605 

3.8391 

24 

37 

1874  5.3349 

2056 

4.8644 

2238 

4.4676 

2422 

4.1282 

2608 

3.8345 

23 

38 

1877  5.3263 

2059 

4.8573 

2241 

4.4615 

2425 

4.1230 

2611 

3.8299 

22 

39 

1880  5.3178 

2062 

4.8501 

2244 

4.4555 

2428 

4.1178 

2614 

3.8254 

21 

40 

1883  5.3093 

2065 

4.8430 

2247 

4.4494 

2432 

4.1126 

2617 

3.8208 

20 

41 

1887  5.3008 

2068 

4.8359 

2251 

4.4434 

2435 

4.1074 

2620 

3.8163 

19 

42 

1890  5.2924 

2071 

4.8288 

2254 

4.4374 

2438 

4.1022 

2623 

3.8118 

18 

43 

1893  5.2839 

2074 

4.8218 

2257 

4.4313 

2441 

4.0970 

2627 

3.8073 

17 

44 

18%  5.2755 

2077 

4.8147 

2260 

4.4253 

2444 

4.0918 

2630 

3.8028 

16 

45 

1899  5.2672 

2080 

4.8077 

2263 

4.4194 

2447 

4.0867 

2633 

3.7983 

15 

46 

1902  5.2588 

2083 

4.8007 

2266 

4.4134 

2450 

4.0815 

2636 

3.7938 

14 

47 

1905  5.2505 

2086 

4.7937 

2269 

4.4075 

2453 

4.0764 

2639 

3.7893 

13 

48 

1908  5.2422 

2089 

4.7867 

2272 

4.4015 

2456 

4.0713 

2642 

3.7848 

12 

49 

1911  5.2339 

2092 

4.7798 

2275 

4.3956 

2459 

4.0662 

2645 

3.7804 

11 

50 

1914  5.2257 

2095 

4.7729 

2278 

43897 

2462 

4.0611 

2648 

3.7760 

10 

51 

1917  5.2174 

2098 

4.7659 

2281 

4.3838 

2465 

4.0560 

2651 

3.7715 

9 

52 

1920  5.2092 

2101 

4.7591 

2284 

4.3779 

2469 

4.0509 

2655 

3.7671 

8 

53 

1923  5.2011 

2104 

4.7522 

2287 

4.3721 

2472 

4.0459 

2658 

3.7627 

7 

54 

1926  5.1929 

2107 

4.7453 

2290 

4.3662 

2475 

4.0408 

2661 

3.7583 

6 

55 

1929  5.1848 

2110 

4.7385 

2293 

4.3604 

2478 

4.0358 

2664 

3.7539 

5 

56 

1932  5.1767 

2113 

4.7317 

22% 

4.3546 

2481 

4.0308 

2667 

3.7495 

4 

57 

1935  5.1686 

2116 

4.7249 

2299 

4.3488 

2484 

4.0257 

2670 

3.7451 

3 

58 

1938  5.1606 

2119 

4.7181 

2303 

4.3430 

2487 

4.0207 

2673 

3.7408 

2 

59 

1941  5.1526 

2123 

4.7114 

2306 

4.3372 

2490 

4.0158 

2676 

3.7364 

1 

60 

1944  5.1446 

2126 

4.7046 

2309 

4.3315 

2493 

4.0108 

2679 

3.7321 

0 

cot   tan 
79° 

cot   tan 
78° 

cot   tan 

77° 

cot   tan 
76° 

cot  tan 

75° 

f 

f 

' 


64 

NATURAL  TANGENTS  AND 

COTANGENTS. 

f 

15° 

16° 

17° 

18° 

19° 

r 

tan 

cot 

tan 

cot 

tan 

cot 

tAn 

cot 

tan 

cot 

O 

2679 

3.7321 

2867 

3.4874 

3057 

3.2709 

3249 

3.0777 

3443 

2.9042 

60 

1 

2683 

3.7277 

2871 

3.4836 

3060 

3.2675 

3252 

3.0746 

3447 

2.9015 

59 

2 

2686 

3.7234 

2874 

3.4798 

3064 

3.2641 

3256 

3.0716 

3450 

2.8987 

58 

3 

2689 

3.7191 

2877 

3.4760 

3067 

3.2607 

3259 

3.0686 

3453 

2.8960 

57 

4 

2692 

3.7148 

2880 

3.4722 

3070 

3.2573 

3262 

3.0655 

3456 

2.8933 

56 

5 

2695 

3.7105 

2883 

3.4684 

3073 

3.2539 

3265 

3.0625 

3460 

2.8905 

55 

6 

2698 

3.7062 

2886 

3.4646 

3076 

3.2506 

3269 

3.0595 

3463 

2.8878 

54 

7 

2701 

3.7019 

2890 

3.4608 

3080 

3.2472 

3272 

3.0565 

3466 

2.8851 

53 

8 

2704 

3.6976 

2893 

3.4570 

3083 

3.2438 

3275 

3.0535 

3469 

2.8824 

52 

9 

2708 

3.6933 

28% 

3.4533 

3086 

3.2405 

3278 

3.0505 

3473 

2.8797 

51 

lO 

2711 

3.6891 

2899 

3.4495 

3089 

3.2371 

3281 

3.0475 

3476 

2.8770 

50 

11 

2714 

3.6848 

2902 

3.4458 

3092 

3.2338 

3285 

3.0445 

3479 

2.8743 

49 

12 

2717 

3.6806 

2905 

3.4420 

3096 

3.2305 

3288 

3.0415 

3482 

2.8716 

48 

13 

2720 

3.6764 

2908 

3.4383 

3099 

3.2272 

3291 

3.0385 

3486 

2.8689 

47 

14 

2723 

3.6722 

2912 

3.4346 

3102 

3.2238 

3294 

3.0^56 

3489 

2.8662 

46 

16 

2726 

3.6680 

2915 

3.4308 

3105 

3.2205 

3298 

3.0326 

3492 

2.8636 

45 

16 

2729 

3.6638 

2918 

3.4271 

3108 

3.2172 

3301 

3.02% 

3495 

2.8609 

44 

17 

2733 

3.65% 

2921 

3.4234 

3111 

3.2139 

3304 

3.0267 

3499 

2.8582 

43 

18 

2736 

3.6554 

2924 

3.4197 

3115 

3.2106 

3307 

3.0237 

3502 

2.8556 

42 

19 

2739 

3.6512 

2927 

3.4160 

3118 

3.2073 

3310 

3.0208 

3505 

2.8529 

41 

20 

2742 

3.6470 

2931 

3.4124 

3121 

3.2041 

3314 

3.0178 

3508 

2.8502 

40 

21 

2745 

3.6429 

2934 

3.4087 

3124 

3.2008 

3317 

3.0149 

3512 

2.8476 

39 

22 

2748 

3.6387 

2937 

3.4050 

3127 

3.1975 

3320 

3.0120 

3515 

2.8449 

38 

23 

2751 

3.6346 

2940 

3.4014 

3131 

3.1943 

3323 

3.0090 

3518 

2.8423 

37 

24 

2754 

3.6305 

2943 

3.3977 

3134 

3.1910 

3327 

3.0061 

3522 

2.8397 

36 

25 

2758 

3.6264 

2946 

3.3941 

3137 

3.1878 

3330 

3.0032 

3525 

2.8370 

35 

26 

2761 

3.6222 

2949 

3.3904 

3140 

3.1845 

3333 

3.0003 

3528 

2.8344 

34 

27 

2764 

3.6181 

2953 

3.3868 

3143 

3.1813 

3336 

2.9974 

3531 

2.8318 

33 

28 

2767 

3.6140 

2956 

3.3832 

3147 

3.1780 

3339 

2.9945 

3535 

2.8291 

32 

29 

2770 

3.6100 

2959 

3.37% 

3150 

3.1748 

3343 

2.9916 

3538 

2.8265 

31 

ao 

2773 

3.6059 

2%2 

3.3759 

3153 

3.1716 

3346 

2.9887 

3541 

2.8239 

30 

31 

2776 

3.6018 

2%5 

3.3723 

3156 

3.1684 

3349 

2.9858 

3544 

2.8213 

29 

32 

2780 

3.5978 

2968 

3.3687 

3159 

3.1652 

3352 

2.9829 

3548 

2.8187 

28 

33 

2783 

3.5937 

2972 

3.3652 

3163 

3.1620 

3356 

2.9800 

3551 

2.8161 

27 

34 

2786 

3.5897 

2975 

3.3616 

3166 

3.1588 

3359 

2.9772 

3554 

2.8135 

26 

35 

2789 

3.5856 

2978 

3.3580 

3169 

3.1556 

3362 

2.9743 

3558 

2.8109 

25 

36 

2792 

3.5816 

2981 

3.3544 

3172 

3.1524 

3365 

2.9714 

3561 

2.8083 

24 

37 

2795 

3.5776 

2984 

3.3509 

3175 

3.1492 

3369 

2.9686 

3564 

2.8057 

23 

38 

2798 

3.5736 

2987 

3.3473 

3179 

3.1460 

3372 

2.%57 

3567 

2.8032 

22 

39 

2801 

3.5696 

2991 

3.3438 

3182 

3.1429 

3375 

2.%29 

3571 

2.8006 

21 

40 

2805 

3.5656 

2994 

3.3402 

3185 

3.1397 

3378 

2.9600 

3574 

2.7980 

20 

41 

2808 

3.5616 

2997 

3.3367 

3188 

3.1366 

3382 

2.9572 

3577 

2.7955 

19 

42 

2811 

3.5576 

3000 

3.3332 

3191 

3.1334 

3385 

2.9544 

3581 

2.7929 

18 

43 

2814 

3.5536 

3003 

3.3297 

3195 

3.1303 

3388 

2.9515 

3584 

2.7903 

17 

44 

2817 

3.5497 

3006 

3.3261 

3198 

3.1271 

3391 

2.9487 

3587 

2.7878 

16 

45 

2820 

3.5457 

3010 

3.3226 

3201 

3.1240 

3395 

2.9459 

3590 

2.7852 

15 

46 

2823 

3.5418 

3013 

3.3191 

3204 

3.1209 

3398 

2.9431 

3594 

2.7827 

14 

47 

2827 

3.5379 

3016 

3.3156 

3207 

3.1178 

3401 

2.9403 

3597 

2.7801 

13 

48 

2830 

3.5339 

3019 

3.3122 

3211 

3.1146 

3404 

2.9375 

3600 

2.7776 

12 

49 

2833 

3.5300 

3022 

3.3087 

3214 

3.1115 

3408 

2.9347 

3604 

2.7751 

11 

50 

2836 

3.5261 

3026 

3.3052 

3217 

3.1084 

3411 

2.9319 

3607 

2.7725 

lO 

51 

2839 

3.5222 

3029 

3.3017 

3220 

3.1053 

3414 

2.9291 

3610 

2.7700 

9 

52 

2842 

3.5183 

3032 

3.2983 

3223 

3.1022 

3417 

2.9263 

3613 

2.7675 

8 

53 

2845 

3.5144 

3035 

3.2948 

3227 

3.0991 

3421 

2.9235 

3617 

2.7650 

7 

54 

2849 

3.5105 

3038 

3.2914 

3230 

3.0%1 

3424 

2.9208 

3620 

2.7625 

6 

55 

2852 

3.5067 

3041 

3.2880 

3233 

3.0930 

3427 

2.9180 

3623 

2.7600 

5 

56 

2855 

3.5028 

3045 

3.2845 

3236 

3.0899 

3430 

2.9152 

3627 

2.7575 

4 

57 

2858 

3.4989 

3048 

3.2811 

3240 

3.0868 

3434 

2.9125 

3630 

2.7550 

3 

58 

2861 

3.4951 

3051 

3.2777 

3243 

3.0838 

3437 

2.9097 

3633 

2.7525 

2 

59 

2864 

3.4912 

3054 

3.2743 

3246 

3.0807 

3440 

2.9070 

3636 

2.7500 

1 

60 

2867 

3.4874 

3057 

3.2709 

3249 

3.0777 

3443 

2.9042 

3640 

2.7475 

O 

cot   tao 

74° 

cot   tan 
73° 

cot   tan 

72° 

cot   tan 
710 

cot  tan 
70° 

f 

f 

NATURAL  TANGENTS  AND  COTANGENTS. 


65 


o 

1 

2 
3 
4 

5 

6 

7 
8 
9 

lO 

11 
12 
13 
14 

15 

16 
17 
18 
19 

20 

21 
22 
23 
24 

25 

26 
27 

28 
29 

30 

31 
32 

34 

35 

36 
37 
38 
39 

40 

41 
42 
43 
44 

45 

46 
47 
48 
49 

50 

51 
52 
53 
54 

55 

56 
57 
58 
59 

60 


20^ 


21° 


22 


o 


23^ 


24c 


tan 

3640 
3643 
3646 
3650 
3653 
3656 
3659 
3663 
3666 
3669 
3673 
3676 
3679 
3683 
3686 

3689 
3693 
3696 
3699 
3702 

3706 
3709 
3712 
3716 
3719 
3722 
3726 
3729 
3732 
3736 
3739 
3742 
3745 
3749 
3752 

3755 
3759 
3762 
3765 
3769 

3772 
3775 
3779 
3782 
3785 

3789 
3792 
3795 
3799 
3802 

3805 
3809 
3812 
3815 
3819 
3822 
3825 
3829 
3832 
3835 

3839 
cot 


cot 

2.7475 
2.7450 
2.7425 
2.7400 
2.7376 

2.7351 
2.7326 
2.7302 
2.7277 
2.7253 

2.7228 
2.7204 
2.7179 
2.7155 
2.7130 

2.7106 
2.7082 
2.7058 
2.7034 
2.7009 

2.6985 
2.6961 
2.6937 
2.6913 
2.6889 
2.6865 
2.6841 
2.6818 
2.6794 
2.6770 

2.6746 
2.6723 
2.6699 
2.6675 
2.6652 

2.6628 
2.6605 
2.6581 
2.6558 
2.6534 

2.6511 
2.6488 
2.6464 
2.6441 
2.6418 

2.6395 
2.6371 
2.6348 
2.6325 
2.6302 

2.6279 
2.6256 
2.6233 
2.6210 
2.6187 

2.6165 
2.6142 
2.6119 
2.60% 
2.6074 

2.6051 
tan 


60' 


tan 

3839 
3842 
3845 
3849 

3852 

3855 
3859 
3862 
3865 
3869 
3872 
3875 
3879 
3882 
3885 

3889 
3892 
3895 
3899 
3902 

3906 
3909 
3912 
3916 
3919 
3922 
3926 
3929 
3932 
3936 

3939 
3942 
3946 
3949 
3953 
3956 
3959 
3%3 
3966 
3969 

3973 
3976 
3979 
3983 
3986 
3990 
3993 
39% 
4000 
4003 
4006 
4010 
4013 
4017 
4020 

4023 
4027 
4030 
4033 
4037 
4040 
cot 


cot 

2.6051 
2.6028 
2.6006 
2.5983 
2.5961 
2.5938 
2.5916 
2.5893 
2.5871 
2.5848 
2.5826 
2.5804 
2.5782 
2.5759 
2.5737 

2.5715 
2.5693 
2.5671 
2.5649 
2.5627 

2.5605 
2.5533 
2.5561 
2.5539 
2.5517 
2.5495 
2.5473 
2.5452 
2.5430 
2.5408 

2.5386 
2.5365 
2.5343 
2.5322 
2.5300 
2.5279 
2.5257 
2.5236 
2.5214 
2.5193 
2.5172 
2.5150 
2.5129 
2.5108 
2.5086 

2.5065 
2.5044 
2.5023 
2.5002 
2.4981 
2.4960 
2.4939 
2.4918 
2.4897 
2.4876 

2.4855 
2.4834 
2.4813 
2.4792 
2.4772 

2.4751 
tan 


68^ 


tan 

4040 
4044 
4047 
4050 
4054 

4057 
4061 
4064 
4067 
4071 
4074 
4078 
4081 
4084 
4088 

4091 
4095 
4098 
4101 
4105 

4108 
4111 
4115 
4118 
4122 

4125 
4129 
4132 
4135 
4139 
4142 
4146 
4149 
4152 
4156 

4159 
4163 
4166 
4169 
4173 
4176 
4180 
4183 
4187 
4190 

4193 
4197 
4200 
4204 
4207 
4210 
4214 
4217 
4221 
4224 

4228 
4231 
4234 
4238 
4241 

4245 
cot 


cot 

2.4751 
2.4730 
2.4709 
2.4689 
2.4668 
2.4648 
2.4627 
2.4606 
2.4586 
2.4566 

2.4545 
2.4525 
2.4504 
2.4484 
2.4464 

2.4443 
2.4423 
2.4403 
2.4383 
2.4362 
2.4342 
2.4322 
2.4302 
2.4282 
2.4262 

2.4242 
2.4222 
2.4202 
2.4182 
2.4162 

2.4142 
2.4122 
2.4102 
2.4083 
2.4063 
2.4043 
2.4023 
2.4004 
2.3984 
2.3964 

2.3945 
2.3925 
2.3906 
2.3886 
2.3867 

2.3847 
2.3828 
2.3808 
2.3789 
2.3770 

2.3750 
2.3731 
2.3712 
2.3693 
2.3673 

2.3654 
2.3635 
2.3616 
2.3597 
2.3578 

2.3559 
tan 


67^ 


tan   cot 

4245  2.3559 

4248  2.3539 

4252  2.3520 

4255  2.3501 

4258  2.3483 


4262 
4265 
4269 
4272 
4276 

4279 
4283 
4286 
4289 
4293 

42% 
4300 
4303 
4307 
4310 
4314 
4317 
4320 
4324 
4327 
4331 
4334 
4338 
4341 
4345 

4348 
4352 
4355 
4359 
4362 

4365 
4369 
4372 
4376 
4379 

4383 
4386 
4390 
4393 
4397 
4400 
4404 
4407 
4411 
4414 

4417 
4421 
4424 
4428 
4431 

4435 
4438 
4442 
4445 
4449 

4452 
cot 


2.3464 
2.3445 
2.3426 
2.3407 
2.3388 

2.3369 
2.3351 
2.3332 
2.3313 
2.3294 

2.3276 
2.3257 
2.3238 
2.3220 
2.3201 

2.3183 
2.3164 
2.3146 
2.3127 
2.3109 

2.3090 

2.3072 

2.3053 

2.3035 

2.301> 

2.2998 

2.2980 

2.2962 

2.2944 

2.2925 

2.2907 
2.2889 
2.2871 
2.2853 
2.2835 

2.2817 
2.2799 
2.2781 
2.2763 
2.2745 

2.2727 
2.2709 
2.2691 
2.2673 
2.2655 

2.2637 
2.2620 
2.2602 
2.2584 
2.2566 

2.2549 
2.2531 
2.2513 
2.24% 
2.2478 

2.2460 
tan 


66"= 


tan 

4452 
4456 
4459 
4463 
4466 

4470 
4473 
4477 
4480 
4484 

4487 
4491 
4494 
4498 
4501 

4505 
4508 
4512 
4515 
4519 
4522 
4526 
4529 
4533 
4536 
4540 
4543 
4547 
45.S0 
4554 

4557 
4561 
4564 
4568 
4571 

4575 
4578 
4582 
4585 
4589 
4592 
45% 
4599 
4603 
4607 
4610 
4614 
4617 
4621 
4624 

4628 
4631 
4635 
4638 
4642 

4645 
4649 
4652 
4656 
4660 

4663 
cot 


cot 

2.2460 
2.2443 
2.2425 
2.2408 
2.2390 

2.2373 
2.2355 
2.2338 
2.2320 
2.2303 

2.2286 
2.2268 
2.2251 
2.2234 
2.2216 

2.2199 
2.2182 
2.2165 
2.2148 
2.2130 

2.2113 
2.20% 
2.2079 
2.2062 
2.2045 
2.2028 
2.2011 
2.1994 
2.1977 
2.1960 

2.1943 
2.1926 
2.1909 
2.1892 
2.1876 

2.1859 
2.1842 
2.1825 
2.1508 
2.1792 

2.1775 
2.1758 
2.1742 
2.1725 
2.1708 
2.1692 
2.1675 
2.1659 
2.1642 
2.1625 
2.1609 
2.1592 
2.1576 
2.1560 
2.1543 

2.1527 
2.1510 
2.1494 
2.1478 
2.1461 

2.1445 
tan 


65^ 


60 

59 

58 
57 
56 

55 

54 
53 

52 
51 

50 

49 
48 
47 
46 

45 

44 
43 
42 
41 

40 

39 
38 
37 
36 

35 

34 
ZZ 
32 
31 

30 

29 
28 
27 
26 

25 

24 
23 
22 
21 

20 

19 
18 
17 
16 

15 

14 
13 
12 
11 

10 

9 
8 
7 
6 

5 

4 
3 
2 

1 

O 


66 


NATURAL  TANGENTS  AND  COTANGENTS. 


!l 


f 

25*^ 

26*^ 

27° 

28° 

29° 

f 

tan  cot 

tan   cot 

tan   cot 

tan   cot 

tan   cot 

o 

4663  2.1445 

4877  2.0503 

5095  l.%26 

5317  1.8807 

5543  1.8040 

60 

1 

4667  2.1429 

4881  2.0488 

5099  l.%12 

5321  1.8794 

5547  1.8028 

59 

2 

4670  2.1413 

4885  2.(H73 

5103  1.9598 

5325  1.8781 

5551  1.8016 

58 

3 

4674  2.1396 

4888  2.0+58 

5106  1.9584 

5328  1.8768 

5555  1.8003 

57 

4 

4677  2.1380 

4892  2.0443 

5110  1.9570 

5332  1.8755 

5558  1.7991 

56 

5 

4681  2.1364 

4895  2.0428 

5114  1.9556 

5336  1.8741 

5562  1.7979 

55 

6 

4684  2.1348 

4899  2.(H13 

5117  1.9542 

5340  1.8728 

5566  1.7966 

54 

7 

4688  2.1332 

4903  2.0398 

5121  1.9528 

5343  1.8715 

5570  1.7954 

53 

8 

4691  2.1315 

4906  2.0383 

5125  1.9514 

5347  1.8702 

5574  1.7942 

52 

9 

4695  2.1299 

4910  2.0368 

5128  1.9500 

5351  1.8689 

5577  1.7930 

51 

lO 

4699  2.1283 

4913  2.0353 

5132  1.9486 

5354  1.8676 

5581  1.7917 

50 

11 

4702  2.1267 

4917  2.0338 

5136  1.9472 

5358  1.8663 

5585  1.7905 

49 

12 

4706  2.1251 

4921  2.0323 

5139  1.9458 

5362  1.8650 

5589  1.7893 

48 

13 

4709  2.1235 

4924  2.0308 

5143  1.9444 

5366  1.8637 

5593  1.7881 

47 

14 

4713  2.1219 

4928  2.0293 

5147  1.9+30 

5369  1.8624 

55%  1.7868 

46 

16 

4716  2.1203 

4931  2.0278 

5150  1.9416 

5373  1.8611 

5600  1.7856 

45 

16 

4720  2.1187 

4935  2.0263 

5154  1.9402 

5377  1.8598 

560+  1.7844 

44 

17 

4723  2.1171 

4939  2.0248 

5158  1.9388 

5381  1.8585 

5608  1.7832 

43 

18 

4727  2.1155 

4942  2.0233 

5161  1.9375 

5384  1.8572 

5612  1.7820 

42 

19 

4731  2.1139 

4946  2.0219 

5165  1.9361 

5388  1.8559 

5616  1.7808 

41 

20 

4734  2.1123 

4950  2.0204 

5169  1.9347 

5392  1.8546 

5619  1.77% 

40 

21 

4738  2.1107 

4953  2.0189 

5172  1.9333 

53%  1.8533 

5623  1.7783 

39 

22 

4741  2.1092 

4957  2.0174 

5176  1.9319 

5399  1.8520 

5627  1.7771 

38 

23 

4745  2.1076 

4960  2.0160 

5180  1.9306 

5403  1.8507 

5631  1.7759 

37 

24 

4748  2.1060 

496+  2.0145 

5184  1.9292 

5407  1.8495 

5635  1.7747 

36 

25 

4752  2.10H 

4968  2.0130 

5187  1.9278 

5411  1.8482 

5639  1.7735 

85 

26 

4755  2.1028 

4971  2.0115 

5191  1.9265 

5415  1.8469 

5642  1.7723 

34 

27 

4759  2.1013 

4975  2.0101 

5195  1.9251 

5418  1.8456 

5646  1.7711 

33 

28 

4763  2.0997 

4979  2.0086 

5198  1.9237 

5422  1.8443 

5650  1.7699 

32 

29 

4766  2.0981 

4982  2.0072 

5202  1.9223 

5426  1.8430 

5654  1.7687 

31 

SO 

4770  2.0%5 

4986  2.0057 

5206  1.9210 

5430  1.8418 

5658  1.7675 

30 

31 

4773  2.0950 

4989  2.0042 

5209  1.91% 

5433  1.8405 

5662  1.7663 

29 

32 

4777  2.0934 

4993  2.0028 

5213  1.9183 

5437  1.8392 

5665  1.7651 

28 

33 

4780  2.0918 

4997  2.0013 

5217  1.9169 

5441  1.8379 

5669  1.7639 

27 

34 

4784  2.0903 

5000  1.9999 

5220  1.9155 

5445  1.8367 

5673  1.7627 

26 

35 

4788  2.0887 

5004  1.9984 

5224  1.9142 

5448  1.8354 

5677  1.7615 

25 

36 

4791  2.0872 

5008  1.9970 

5228  1.9128 

5452  1.8341 

5681  1.7603 

24 

37 

4795  2.0856 

5011  1.9955 

5232  1.9115 

5456  1.8329 

5685  1.7591 

23 

38 

4798  2.0840 

5015  1.9941 

5235  1.9101 

5460  1.8316 

5688  1.7579 

22 

39 

4802  2.0825 

5019  1.9926 

5239  1.9088 

5464  1.8303 

5692  1.7567 

21 

40 

4806  2.0809 

5022  1.9912 

5243  1.9074 

5467  1.8291 

56%  1.7556 

20 

41 

4809  2.0794 

5026  1.9897 

5246  1.9061 

5471  1.8278 

5700  1.7544 

19 

42 

4813  2.0778 

5029  1.9883 

5250  1.9047 

5475  1.8265 

5704  1.7532 

18 

43 

4816  2.0763 

5033  1.9868 

5254  1.9034 

5479  1.8253 

5708  1.7520 

17 

44 

4820  2.0748 

5037  1.9854 

5258  1.9020 

5482  1.8240 

5712  1.7508 

16 

45 

4823  2.0732 

5(H0  1.9840 

5261  1.9007 

5486  1.8228 

5715  1.74% 

15 

46 

4827  2.0717 

50H  1.9825 

5265  1.8993 

5490  1.8215 

5719  1.7485 

14 

47 

4831  2.0701 

5048  1.9811 

5269  1.8980 

5494  1.8202 

5723  1.7473 

13 

48 

4834  2.0686 

5051  1.9797 

5272  1.8%7 

5498  1.8190 

5727  1.7461 

12 

49 

4838  2.0671 

5055  1.9782 

5276  1.8953 

5501  1.8177 

5731  1.7449 

11 

50 

4841  2.0655 

5059  1.9768 

5280  1.8940 

5505  1.8165 

5735  1.7437 

lO 

51 

4845  2.0640 

5062  1.9754 

5284  1.8927 

5509  1.8152 

5739  1.7426 

9 

52 

4849  2.0625 

5066  1.9740 

5287  1.8913 

5513  1.8140 

5743  1.7414 

8 

53 

4852  2.0609 

5070  1.9725 

5291  1.8900 

5517  1.8127 

5746  1.7402 

7 

54 

4856  2.0594 

5073  1.9711 

5295  1.8887 

5520  1.8115 

5750  1.7391 

6 

55 

4859  2.0579 

5077  l.%97 

5298  1.8873 

5524  1.8103 

5754  1.7379 

6 

56 

4863  2.0564 

5081  1.9683 

5302  1.8860 

5528  1.8090 

5758  1.7367 

4 

57 

4S67  2.0549 

5084  1.9669 

5306  1.8847 

5532  1.8078 

5762  1.7355 

3 

58 

4870  2.0533 

5088  l.%54 

5310  1.8834 

5535  1.8065 

5766  1.7344 

2 

59 

4874  2.0518 

5092  1.9640 

5313  1.8820 

5539  1.8053 

5770  1.7332 

1 

60 

4877  2.0503 

5095  l.%26 

5317  1.8807 

5543  1.80+0 

5774  1.7321 

O 

cot   tan 
64° 

cot   tan 
63° 

cot   tan 
62° 

cot   tan 
61° 

cot   tan 
60° 

f 

f 

NATURAL  TANGENTS  AND  COTANGENTS. 


67 


f 

30° 

31° 

32° 

33° 

34° 

f 

tan 

cot 

tan 

cot 

tan 

cot 

tan 

cot 

tan 

cot 

o 

5774 

1.7321 

6009 

1.6643 

6249 

1.6003 

6494 

1.5399 

6745 

1.4826 

60 

1 

5777 

1.7309 

6013 

1.6632 

6253 

1.5993 

6498 

1.5389 

6749 

1.4816 

59 

2 

5781 

1.7297 

6017 

1.6621 

6257 

1.5983 

6502 

1.5379 

6754 

1.4807 

58 

3 

5785 

1.7286 

6020 

1.6610 

6261 

1.5972 

6506 

15369 

6758 

1.4798 

57 

4 

5789 

1.7274 

6024 

1.6599 

6265 

1.5962 

6511 

1.5359 

6762 

1.4788 

56 

5 

5793 

1.7262 

6028 

1.6588 

6269 

1.5952 

6515 

1.5350 

6766 

1.4779 

55 

6 

5797 

1.7251 

6032 

1.6577 

6273 

1.5941 

6519 

1.5340 

6771 

1.4770 

54 

7 

5801 

1.7239 

6036 

1.6566 

6277 

1.5931 

6523 

1.5330 

6775 

1.4761 

53 

8 

5805 

1.7228 

6040 

1.6555 

6281 

1.5921 

6527 

1.5320 

6779 

1.4751 

52 

9 

5808 

1.7216 

6044 

1.6545 

6285 

1.5911 

6531 

1.5311 

6783 

1.4742 

51 

10 

5812 

1.7205 

6048 

1.6534 

6289 

1.5900 

6536 

1.5301 

6787 

1.4733 

50 

11 

5816 

1.7193 

6052 

1.6523 

6293 

1.5890 

6540 

1.5291 

6792 

1.4724 

49 

12 

5820 

1.7182 

6056 

1.6512 

6297 

1.5880 

6544 

1.5282 

6796 

1.4715 

48 

13 

5824 

1.7170 

6060 

1.6501 

6301 

1.5869 

6548 

1.5272 

6800 

1.4705  ■ 

47 

14 

5828 

1.7159 

6064 

1.6490 

6305 

1.5859 

6552 

1.5262 

6805 

1.46% 

46 

15 

5832 

1.7147 

6068 

1.6479 

6310 

1.5849 

6556 

1.5253 

6809 

1.4687 

45 

16 

5836 

1.7136 

6072 

1.6469 

6314 

1.5839 

6560 

1.5243 

6813 

1.4678 

44 

17 

5840 

1.7124 

6076 

1.6458 

6318 

1.5829 

6565 

1.5233 

6817 

1.4669 

43 

18 

5844 

1.7113 

6080 

1.6447 

6322 

1.5818 

6569 

1.5224 

6822 

1.4659 

42 

19 

5847 

1.7102 

6084 

1.6436 

6326 

1.5808 

6573 

1.5214 

6826 

1.4650 

41 

20 

5851 

1.7090 

6088 

1.6426 

6330 

1.5798 

6577 

1.5204 

6830 

1.4641 

40 

21 

5855 

1.7079 

6092 

1.6415 

6334 

1.5788 

6581 

1.5195 

6834 

1.4632 

39 

22 

5859 

1.7067 

6096 

1.6404 

6338 

1.5778 

6585 

1.5185 

6839 

1.4623 

38 

23 

5863 

1.7056 

6100 

1.6393 

6342 

1.5768 

6590 

1.5175 

6843 

1.4614 

37 

24 

5867 

1.70+5 

6104 

1.6383 

6346 

1.5757 

6594 

1.5166 

6847 

1.4605 

36 

25 

5871 

1.7033 

6108 

1.6372 

6350 

1.5747 

6598 

1.5156 

6851 

1.45% 

35 

26 

5875 

1.7022 

6112 

1.6361 

6354 

1.5737 

6602 

1.5147 

6856 

1.4586 

34 

27 

5879 

1.7011 

6116 

1.6351 

6358 

1.5727 

6606 

1.5137 

6860 

1.4577 

33 

28 

5883 

1.6999 

6120 

1.6340 

6363 

1.5717 

6610 

1.5127 

6864 

1.4568 

32 

29 

5887 

1.6988 

6124 

1.6329 

6367 

1.5707 

6615 

1.5118 

6869 

1.4559 

31 

30 

5890 

1.6977 

6128 

1.6319 

6371 

1.5697 

6619 

1.5108 

6873 

1.4550 

30 

31 

5894 

1.6%5 

6132 

1.6308 

6375 

1.5687 

6623 

1.5099 

6877 

1.4541 

29 

32 

5898 

1.6954 

6136 

1.6297 

6379 

1.5677 

6627 

1.5089 

6881 

1.4532 

28 

33 

5902 

1.6943 

6140 

1.6287 

6383 

1.5667 

6631 

1.5080 

6886 

1.4523 

27 

34 

5906 

1.6932 

6144 

1.6276 

6387 

1.5657 

6636 

1.5070 

6890 

1.4514 

26 

35 

5910 

1.6920 

6148 

1.6265 

6391 

1.5647 

6640 

1.5061 

6894 

1.4505 

25 

36 

5914 

1.6909 

6152 

1.6255 

6395 

1.5637 

6644 

1.5051 

6899 

1.44% 

24 

37 

5918 

1.6898 

6156 

1.6244 

6399 

1.5627 

6648 

1.5042 

6903 

1.4487 

23 

38 

5922 

1.6887 

6160 

1.6234 

6403 

1.5617 

6652 

1.5032 

6907 

1.4478 

22 

39 

5926 

1.6875 

6164 

1.6223 

6408 

1.5607 

6657 

1.5023 

6911 

1.4469 

21 

40 

5930 

1.6864 

6168 

1.6212 

6412 

1.5597 

6661 

1.5013 

6916 

1.4460 

20 

41 

5934 

1.6853 

6172 

1.6202 

6416 

1.5587 

6665 

1.5004 

6920 

1.4451 

19 

42 

5938 

1.6842 

6176 

1.6191 

6420 

1.5577 

6669 

1.4994 

6924 

1.4442 

18 

43 

5942 

1.6831 

6180 

1.6181 

6424 

1.5567 

6673 

1.4985 

6929 

1.4+33 

17 

44 

5945 

1.6820 

6184 

1.6170 

6428 

1.5557 

6678 

1.4975 

6933 

1.4424 

16 

45 

5949 

1.6808 

6188 

1.6160 

6432 

1.5547 

6682 

1.4966 

6937 

1.4415 

15 

46 

5953 

1.6797 

6192 

1.6149 

6436 

1.5537 

6686 

1.4957 

6942 

1.4+06 

14 

47 

5957 

1.6786 

6196 

1.6139 

6440 

1.5527 

6690 

1.4947 

6946 

1.4397 

13 

48 

5%1 

1.6775 

6200 

1.6128 

6445 

1.5517 

6694 

1.4938 

6950 

1.4388 

12 

49 

5%5 

1.6764 

6204 

1.6118 

6449 

1.5507 

6699 

1.4928 

6954 

1.4379 

11 

50 

5969 

1.6753 

6208 

1.6107 

6453 

1.5497 

6703 

1.4919 

6959 

1.4370 

lO 

51 

5973 

1.6742 

6212 

1.6097 

6457 

1.5487 

6707 

1.4910 

6963 

1.4361 

9 

52 

5977 

1.6731 

6216 

1.6087 

6461 

1.5477 

6711 

1.4900 

6967 

1.4352 

8 

53 

5981 

1.6720 

6220 

1.6076 

6465 

1.5468 

6716 

1.4891 

6972 

1.4344 

7 

54 

5985 

1.6709 

6224 

1.6066 

6469 

1.5458 

6720 

1.4882 

6976 

1.4335 

6 

55 

5989 

1.6698 

6228 

1.6055 

6473 

1.5448 

6724 

1.4872 

6980 

1.4326 

5 

56 

^  am 

5993 

1.6687 

6233 

1.6045 

6478 

1.5438 

6728 

1.4863 

6985 

1.4317 

4 

57 

5997 

1.6676 

6237 

1.6034 

6482 

1.5428 

6732 

1.4854 

6989 

1.4308 

3 

58 

6001 

1.6665 

6241 

1.6024 

6486 

1.5418 

6737 

1.4844 

6993 

1.4299 

2 

59 

6005 

1.6654 

6245 

1.6014 

6490 

1.5408 

6741 

1.4835 

6998 

1.4290 

1 

60 

6009 

1.6643 

6249 

1.6003 

6494 

1.5399 

6745 

1.4826 

7002 

1.4281 

O 

f 

cot   tan 
59° 

cot   tan 
58° 

cot   tan 

57° 

cot   tan 
56° 

cot  tan 
55° 

f 

^ 


t:  I 

i 


It 

''. 

( 

1 

r 
1 

1 

■iiii 

68 


NATURAL  TANGENTS  AND  COTANGENTS. 


f 

35^ 

36° 

37° 

38° 

3»° 

f 

tan 

cot 

tan   cot 

tan 

cot 

tan   cot 

tan 

cot 

o 

7002 

1.4281 

7265  1.3764 

7536 

1.3270 

7813  1.2799 

8098 

1.2349 

GO 

1 

7006 

1.4273 

7270  1.3755 

7540 

1.3262 

7818  1.2792 

8103 

1.2342 

59 

2 

7011 

1.4264 

7274  1.3747 

7545 

1.3254 

7822  1.2784 

8107 

1.2334 

58 

3 

7015 

1.4255 

7279  1.3739 

7549 

1.3246 

7827  1.2776 

8112 

1.2327 

57 

4 

7019 

1.4246 

7283  1.3730 

7554 

1.3238 

7832  1.2769 

8117 

1.2320 

56 

5 

7024 

1.4237 

7288  1.3722 

7558 

1.3230 

7836  1.2761 

8122 

1.2312 

55 

6 

7028 

1.4229 

7292  1.3713 

7563 

1.3222 

7841  1.2753 

8127 

1.2305  - 

54 

7 

7032 

1.4220 

7297  1.3705 

7568 

1.3214 

7846  1.2746 

8132 

1.2298 

53 

8 

7037 

1.4211 

7301  1.3697 

7572 

1.3206 

7850  1.2738 

8136 

1.2290 

52 

9 

7(H1 

1.4202 

7306  1.3688 

7577 

1.3198 

7855  1.2731 

8141 

1.2283 

51 

lO 

7(M6 

1.4193 

7310  1.3680 

7581 

1.3190 

7860  1.2723 

8146 

1.2276 

50 

11 

7050 

1.4185 

7314  1.3672 

7586 

1.3182 

7865  1.2715 

8151 

1.2268 

49 

12 

7054 

1.4176 

7319  1.3663 

7590 

1.3175 

7869  1.2708 

8156 

1.2261 

48 

13 

7059 

1.4167 

7323  1.3655 

7595 

1.3167 

7874  1.2700 

8161 

1.2254 

47 

14 

7063 

1.4158 

7328  1.3647 

7600 

1.3159 

7879  1.2693 

8165 

1.2247 

46 

16 

7067 

1.4150 

7332  1.3638 

7604 

1.3151 

788.3  1.2685 

8170 

1.2239 

45 

16 

7072 

1.4141 

7337  1.3630 

7609 

1.3143 

7888  1.2677 

8175 

1.2232 

44 

17 

7076 

1.4132 

7341  1.3622 

7613 

1.3135 

7893  1.2670 

8180 

1.2225 

43 

18 

7080 

1.4124 

7346  1.3613 

7618 

1.3127 

7898  1.2662 

8185 

1.2218 

42 

19 

7085 

1.4115 

7350  1.3605 

7623 

1.3119 

7902  1.2655 

8190 

1.2210 

41 

20 

7089 

1.4106 

7355  1.3597 

7627 

1.3111 

7907  1.2647 

8195 

1.2203 

40 

21 

7091 

1.4097 

7359  1.3588 

7632 

1.3103 

7912  1.2640 

8199 

1.21% 

39 

22 

7098 

1.4089 

736f  1.3580 

7636 

1.3095 

7916  1.2632 

8204 

1.2189 

38 

23 

7102 

1.4080 

7368  1.3572 

7641 

1.3087 

7921  1.2624 

8209 

1.2181 

37 

24 

7107 

1.4071 

7373  1.3564 

7646 

1.3079 

7926  1.2617 

8214 

1.2174 

36 

25 

7111 

1.4063 

7377  1.3555 

7650 

1.3072 

7931  1.2609 

8219 

1.2167 

35 

26 

7115 

1.4054 

7382  1.3547 

7655 

1.3064 

7935  1.2602 

8224 

1.2160 

34 

27 

7120 

1.4(H5 

7386  1.3539 

7659 

1.3056 

7940  1.2594 

8229 

1.2153 

33 

28 

7124 

1.4037 

7391  1.3531 

7664 

1.3048 

7945  1.2587 

8234 

1.2145 

32 

29 

7129 

1.4028 

7395  1.3522 

7669 

1.3040 

7950  1.2579 

8238 

1.2138 

31 

30 

7133 

1.4019 

7400  1.3514 

7673 

1.3032 

7954  1.2572 

8243 

1.2131 

30 

31 

7137 

1.4011 

7404  1.3506 

7678 

1.3024 

7959  1.2564 

8248 

1.2124 

29 

32 

7142 

1.4002 

7409  1.3498 

7683 

1.3017 

7964  1.2557 

8253 

1.2117 

28 

33 

7146 

1.3994 

7413  1.3490 

7687 

1.3009 

7969  1.2549 

8258 

1.2109 

27 

34 

7151 

1.3985 

7418  1.3481 

7692 

1.3001 

7973  1.2542 

8263 

1.2102 

26 

35 

7155 

1.3976 

7422  1.3473 

76% 

1.2993 

7978  1.2534 

8268 

1.2095 

26 

36 

7159 

1J968 

7427  1.3465 

7701 

1.2985 

7983  1.2527 

8273 

1.2088 

24 

37 

7164 

1.3959 

7431  1.3457 

7706 

1.2977 

7988  1.2519 

8278 

1.2081 

23 

38 

7168 

1.3951 

7436  1.3449 

7710 

1.2970 

7992  1.2512 

8283 

1.2074 

22 

39 

7173 

1.3942 

7440  1.3440 

7715 

1.2%2 

7997  1.2504 

8287 

1.2066 

21 

40 

7177 

1.3934 

7445  1.3432 

7720 

1.2954 

8002  1.2497 

8292 

1.2059 

20 

41 

7181 

1.3925 

7449  1.3424 

7724 

1.2946 

8007  1.2489 

8297 

1.2052 

19 

42 

7186 

1.3916 

7454  1.3416 

7729 

1.2938 

8012  1.2482 

8302 

1.2045 

18 

43 

7190 

1.3908 

7458  1.3408 

7734 

1.2931 

8016  1.2475 

8307 

1.2038 

17 

44 

7195 

1.3899 

7463  1.3400 

7738 

1.2923 

8021  1.2467 

8312 

1.2031 

16 

45 

7199 

1.3891 

7467  1.3392 

7743 

1.2915 

8026  1.2460 

8317 

1.2024 

16 

46 

7203 

1.3882 

7472  1.3384 

7747 

1.2907 

8031  1.2452 

8322 

1.2017 

14 

47 

7208 

1.3874 

7476  1.3375 

7752 

1.2900 

8035  1.2445 

8327 

1.2009 

13 

48 

7212 

1.3865 

7481  1.3367 

7757 

1.2892 

8040  1.2437 

8332 

1.2002 

12 

49 

7217 

1.3857 

7485  1.3359 

7761 

1.2884 

8045  1.2430 

8337 

1.1995 

11 

50 

7221 

1.3848 

7490  1.3351 

7766 

1.2876 

8050  1.2423 

8342 

1.1988 

lO 

51 

7226 

1.3840 

7495  1.3343 

7771 

1.2869 

8055  1.2415 

8346 

1.1981 

9 

52 

7230 

1.3831 

7499  1.3335 

7775 

1.2861 

8059  1.2408 

8351 

1.1974 

8 

Mm 

53 

7234 

1.3823 

7504  1.3327 

7780 

1.2853 

8064  1.2401 

8356 

1.1%7 

7 

54 

7239 

1.3814 

7508  1.3319 

7785 

1.2846 

8069  1.2393 

8361 

1.1960 

6 

55 

7243 

1.3806 

7513  1.3311 

7789 

1.2838 

8074  1.2386 

8366 

1.1953 

5 

56 

7248 

1.3798 

7517  1.3303 

7794 

1.2830 

8079  1.2378 

8371 

1.1946 

4 

57 

7252 

1.3789 

7522  1.3295 

7799 

1.2822 

8083  1.2371 

8376 

1.1939 

3 

58 

7257 

1.3781 

7526  1.3287 

7803 

1.2815 

8088  1.2364 

8381 

1.1932 

2 

59 

7261 

1.3772 

7531  1.3278 

7808 

1.2807 

8093  1.2356 

8386 

1.1925 

1 

60 

7265 

1.3764 

7536  1.3270 

7813 

1.2799 

8098  1.2349 

8391 

1.1918 

o 

cot   tan 

64° 

cot   tan 
53° 

cot   tan 
62° 

cot   tan 
51° 

cot  tan 
50° 

__J 

t 

LI 

NATURAL  TANGENTS  AND  COTANGENTS. 


69 


f 

40° 

41° 

42° 

43° 

44° 

f 

tan  cot 

tan 

cot 

tan 

cot 

tan   cot 

tan 

cot 

0 

8391  1.1918 

8693 

1.1504 

9004 

1.1106 

9325  1.0724 

%57 

1.0355 

60 

1 

8396  1.1910 

8698 

1.1497 

9009 

1.1100 

9331  1.0717 

9663 

1.0349 

59 

2 

8401  1.1903 

8703 

1.1490 

9015 

1.1093 

9336  1.0711 

9668 

1.0343 

58 

3 

8406  1.18% 

8708 

1.1483 

9020 

1.1087 

9341  1.0705 

9674 

1.0337 

57 

4 

8411  1.1889 

8713 

1.1477 

9025 

1.1080 

9347  1.0699 

%79 

1.0331 

56 

5 

8416  1.1882 

8718 

1.1470 

9030 

1.1074 

9352  1.0692 

9685 

1.0325 

55 

6 

8421  1.1875 

8724 

1.1463 

9036 

1.1067 

9358  1.0686 

9691 

1.0319 

54 

7 

8426  1.1868 

8729 

1.1456 

9041 

1.1061 

9363  1.0680 

%% 

1.0313 

53 

8 

8431  1.1861 

8734 

1.1450 

9046 

1.1054 

9369  1.0674 

9702 

1.0307 

52 

9 

8436  1.1854 

8739 

1.1443 

9052 

1.1048 

9374  1.0668 

9708 

1.0301 

51 

lO 

8441  1.1847 

8744 

1.1436 

9057 

1.1041 

9380  1.0661 

9713 

1.0295 

60 

11 

8446  1.1840 

8749 

1.1430 

9062 

1.1035 

9385  1.0655 

9719 

1.0289 

49 

12 

8451  1.1833 

8754 

1.1423 

9067 

1.1028 

9391  1.0649 

9725 

1.0283 

48 

13 

8456  1.1826 

8759 

1.1416 

9073 

1.1022 

9396  1.0643 

9730 

1.0277 

47 

14 

8461  1.1819 

8765 

1.1410 

9078 

1.1016 

9402  1.0637 

9736 

1.0271 

46 

15 

8466  1.1812 

8770 

1.1403 

9083 

1.1009 

9407  1.0630 

9742 

1.0265 

46 

16 

8471  1.1806 

8775 

1.13% 

9089 

1.1003 

9113  1.0624 

9747 

1.0259 

44 

17 

8476  1.1799 

8780 

1.1389 

9094 

1.09% 

9418  1.0618 

9753 

1.0253 

43 

18 

8481  1.1792 

8785 

1.1383 

9099 

1.0990 

9424  1.0612 

9759 

1.0247 

42 

19 

8486  1.1785 

8790 

1.1376 

9105 

1.0983 

9429  1.0606 

9764 

1.0241 

41 

20 

8491  1.1778 

8796 

1.1369 

9110 

1.0977 

9435  1.0599 

9770 

1.0235 

40 

21 

8496  1.1771 

8801 

1.1363 

9115 

1.0971 

9440  1.0593 

9776 

1.0230 

39 

22 

8501  1.1764 

8806 

1.1356 

9121 

1.0964 

9446  1.0587 

9781 

1.0224 

38 

23 

8506  1.1757 

8811 

1.1349 

9126 

1.0958 

9451  1.0581 

9787 

1.0218 

37 

24 

8511  1.1750 

8816 

1.1343 

9131 

1.0951 

9457  1.0575 

9793 

1.0212 

36 

25 

8516  1.1743 

8821 

1.1336 

9137 

1.0945 

9462  1.0569 

9798 

1.0206 

35 

26 

8521  1.1736 

8827 

1.1329 

9142 

1.0939 

9468  1.0562 

9804 

1.0200 

34 

27 

8526  1.1729 

8832 

1.1323 

9147 

1.0932 

9473  1.0556 

9810 

1.0194 

33 

28 

8531  1.1722 

8837 

1.1316 

9153 

1.0926 

9479  1.0550 

9816 

1.0188 

32 

29 

8536  1.1715 

8842 

1.1310 

9158 

1.0919 

9484  1.0544 

9821 

1.0182 

31 

30 

8541  1.1708 

8847 

1.1303 

9163 

1.0913 

9490  1.0538 

9827 

1.0176 

30 

31 

8546  1.1702 

8852 

1.12% 

9169 

1.0907 

9495  1.0532 

9833 

1.0170 

29 

32 

8551  1.1695 

8858 

1.1290 

9174 

1.0900 

9501  1.0526 

9838 

1.0164 

28 

33 

8556  1.1688 

8863 

1.1283 

9179 

1.0894 

9506  1.0519. 

9844 

1.0158 

27 

34 

8561  1.1681 

8868 

1.1276 

9185 

1.0888 

9512  1.0513 

9850 

1.0152 

26 

35 

8566  1.1674 

8873 

1.1270 

9190 

1.0881 

9517  1.0507 

9856 

1.0147 

25 

36 

8571  1.1667 

8878 

1.1263 

9195 

1.0875 

9523  1.0501 

9861 

1.0141 

24 

37 

8576  1.1660 

8884 

1.1257 

9201 

1.0869 

9528  1.0495 

9867 

1.0135 

23 

38 

8581  1.1653 

8889 

1.1250 

9206 

1.0862 

9534  1.0489 

9873 

1.0129 

22 

39 

8586  1.1647 

8894 

1.1243 

9212 

1.0856 

9540  1.0483 

9879 

1.0123 

21 

40 

8591  1.1640 

8899 

1.1237 

9217 

1.0850 

9545  1.0477 

9884 

1.0117 

20 

41 

8596  1.1633 

8904 

1.1230 

9222 

1.0843 

9551  1.0470 

9890 

1.0111 

19 

42 

8601  1.1626 

8910 

1.1224 

9228 

1.0837 

9556  1.0464 

98% 

1.0105 

18 

43 

8606  1.1619 

8915 

L1217 

9233 

1.0831 

9562  1.0458 

9902 

1.0099 

17 

44 

8611  1.1612 

8920 

i.1211 

9239 

1.0824 

9567  1.0452 

9907 

1.0094 

16 

45 

8617  U606 

8925 

1.1204 

9244 

1.0818 

9573  1.0446 

9913 

1.0088 

15 

46 

8622  1.1599 

8931 

1.1197 

9249 

1.0812 

9578  1.0440 

9919 

1.0082 

14 

«  0% 

47 

8627  1.1592 

8936 

1.1191 

9255 

1.0805 

9584  l.(H34 

9925 

1.0076 

13 

48 

8632  1.1585 

8941 

1.1184 

9260 

1.0799 

9590  1.0428 

9930 

1.0070 

12 

49 

8637  1.1578 

8946 

1.1178 

9266 

1.0793 

9595  1.0422 

9936 

1.0064 

11 

50 

8642  1.1571 

8952 

1.1171 

9271 

1.0786 

9601  1.0416 

9942 

1.0058 

lO 

51 

8647  1.1565 

8957 

1.1165 

9276 

1.0780 

9606  1.0410 

9948 

1.0052 

9 

52 

8652  1.1558 

8%2 

1.1158 

9282 

1.0774 

%12  1.0404 

9954 

1.0047 

8 

53 

8657  1.1551 

8967 

1.M52 

9287 

1.0768 

%18  1.0398 

9959 

1.0041 

7 

54 

8662  1.1544 

8972 

1.1145 

9293 

1.0761 

%23  1.0392 

9%5 

1.0035 

6 

56 

8667  1.1538 

8978 

1.1139 

9298 

1.0755 

%29  1.0385 

9971 

1.0029 

5 

56 

8672  1.1531 

8983 

1.1132 

9303 

1.0749 

%34  1.0379 

9977 

1.0023 

4 

4* 

57 

8678  1.1524 

8988 

1.1126 

9309 

1.0742 

9640  1.0373 

9983 

1.0017 

3 

58 

8683  L1517 

8994 

L1119 

9314 

1.0736 

9646  1.0367 

9988 

1.0012 

2 

59 

8688  1.1510 

8999 

1.1113 

9320 

1.0730 

%51  1.0361 

9994 

1.0006 

1 

eo 

8693  1.1504 

9004 

1.1106 

9325 

1.0724 

9657  1.0355 

1.000 

1.0000 

O 

f 

cot   tan 
49° 

cot   tan 
48° 

cot   tan 

47° 

cot   tan 
46° 

cot   tan 
46° 

r 

70 


TABLE  VII.-TKAVEKSE  TABLE. 


I 


i 


BeariDg. 

Distance  1. 

Distance  2. 

Distance  3. 

Distance  4. 

Distance  5. 

Bearing. 

o     f 

Lat.     Dep. 

Lat.      Dep. 

Lat.     Dep. 

Lat.      Dep. 

Lat.     Dep. 

0       f 

015 

1.000  0.0(H 

2.000  0.009 

3.000  O.OU 

4.000  0.017 

5.000  0.022 

89  45 

30 

1.000  0.009 

2.000  0.017 

3.000  0.026 

4.000  0.035 

5.000  O.OH 

30 

45 

1.000  0.013 

2.000  0.026 

3.000  0.039 

4.000  0.052 

5.000  0.065 

15 

1    0 

1.000  0.017 

2.000  0.035 

3.000  0.052 

3.999  0.070 

4.999  0.087 

89   0 

15 

1.000  0.022 

2.000  0.044 

2.999  0.065 

3.999  0.087 

4.999  0.109 

45 

30 

1.000  0.026 

1.999  0.052 

2.999  0.079 

3.999  0.105 

4.998  0.131 

30 

45 

1.000  0.031 

1.999  0.061 

2.999  0.092 

3.998  0.122 

4.998  0.153 

15 

2   0 

0.999  0.035 

1.999  0.070 

2.998  0.105 

3.998  0.140 

4.997  0.174 

88   0 

15 

0.999  0.039 

1.998  0.079 

2.998  0.118 

3.997  0.157 

4.9%  0.1% 

45 

30 

0.999  O.OH 

1.998  0.087 

2.997  0.131 

3.9%  0.174 

4.995  0.218 

30 

45 

0.999  0.(H8 

1.998  0.0% 

2.997  0.144 

3.995  0.192 

4.994  0.240 

15 

3   0 

0.999  0.052 

1.997  0.105 

2.9%  0.157 

3.995  0.209 

4.993  0.262 

87   0 

15 

0.998  0.057 

1.997  0.113 

2.995   0.170 

3.994  0.227 

4.992  0.283 

45 

30 

0.998  0.061 

1.9%  0.122 

2.994  0.183 

3.993  0.244 

4.991   0.305 

30 

45 

0.998  0.065 

1.9%  0.131 

2.994  0.1% 

3.991   0.262 

4.989  0.327 

15 

4   0 

0.998  0.070 

1.995   0.140 

2.993   0.209 

3.990  0.279 

4.988  0.349 

86  0 

15 

0.997  0.074 

1.995   0.148 

2.992  0.222 

3.989  0.2% 

4.986  0.371 

45 

30 

0.997  0078 

1.994  0.157 

2.991   0.235 

3.988  0.314 

4.985  0.392 

30 

45 

0.997  0.083 

1.993  0.166 

2.990  0.248 

3.986  0.331 

4.983  0.414 

15 

5   0 

0.9%  0.087 

1.992  0.174 

2.989  0.261 

3.985  0.349 

4.981  0.436 

85   0 

15 

0.9%  0.092 

1.992  0.183 

2.987  0.275 

3.983  0.366 

4.979  0.458 

45 

30 

0.995  0.0% 

1.991   0.192 

2.986  0.288 

3.982  0.383 

4.977  0.479 

30 

45 

0.995  0.100 

1.990  0.200 

2.985   0.301 

3.980  0.401 

4.975  0.501 

15 

6   0 

0.995  0.105 

1.989  0.209 

2.984  0.314 

3.978  0.418 

4.973  0.523 

84   0 

15 

0.994  0.109 

1.988  0.218 

2.982  0.327 

3.976  0.435 

4.970  0.544 

45 

30 

0.994  0.113 

1.987  0.226 

2.981   0.340 

3.974  0.453 

4.968  0.566 

30 

45 

0.993  0.118 

1.986  0.235 

2.979  0.353 

3.972  0.470 

4.%5  0.588 

15 

7   0 

0.993  0.122 

1.985   0.244 

2.978  0.366 

3.970  0.487 

4.963  0.609 

83   0 

15 

0.992  0.126 

1.984  0.252 

2.976  0.379 

3.968  0.505 

4.960  0.631 

45 

30 

0.991  0.131 

1.983  0.261 

2.974   0.392 

3.966  0.522 

4.957  0.653 

30 

45 

0.991  0.135 

1.982  0.270 

2.973   0.405 

3.963  0.539 

4.954  0.674 

15 

8   0 

0.990  0.139 

1.981   0.278 

2.971   0.418 

3.%1   0.557 

4.951   0.6% 

82   0 

15 

0.990  0.143 

1.979  0.287 

2.%9  0.430 

3.959  0574 

4.948  0.717 

45 

30 

0.989  0.148 

1.978  0.2% 

2.%7   0.443 

3.956  0.591 

4.945  0.739 

30 

45 

0.988  0.152 

1.977   0304 

2.%5   0.456 

3.953  0.608 

4.942  0.761 

15 

9  0 

0.988  0.156 

1.975   0.313 

2.963   0.469 

3.951   0.626 

4.938  0.782 

81    0 

15 

0.987  0.161 

1.974  0.321 

2.%1   0.482 

3.948  0.643 

4.935  0.804 

45 

30 

0.986  0.165 

1.973  0.330 

2.959  0.495 

3.945  0.660 

4.931  0.825 

30 

45 

0.986  0.169 

1.971  0.339 

2.957  0.508 

3.942  0.677 

4.928  0.847 

15 

lO   0 

0.985   0174 

1.970  0.347 

2.954  0.521 

3.939  0.695 

4.924  0.868 

80   0 

15 

0.984  0.178 

1.968  0.356 

2.952   0.534 

3.936  0.712 

4.920  0.890 

45 

30 

0.983  0.182 

l.%7  0.364 

2.950  0.547 

3.933  0.729 

4.916  0.911 

30 

45 

0.982  0187 

l.%5  0.373 

2.947  0.560 

3.930  0.746 

4.912  0.933 

15 

11    0 

0.982  0.191 

l.%3  0.382 

2.945   0.572 

3.927  0.763 

4.908  0.954 

79   0 

15 

0.981  0.195 

l.%2  0.390 

2.942  0.585 

3.923  0.780 

4.904  0.975 

45 

30 

0.980  0.199 

1.960  0.399 

2.940  0.598 

3.920  0.797 

4.900  0.997 

30 

45 

0.979  0.204 

1.958  0.407 

2.937  0  611 

3.916  0.815 

4.895   1.018 

15 

12   0 

0.978  0.208 

1.956  0.416 

2.934   0624 

3.913  0.832 

4.891    l.CHO 

78    0 

15 

0.977  0.212 

1.954  0.424 

2.932  0.637 

3.909  0.849 

4.886   1.061 

45 

30 

0.976  0.216 

1.953  0.433 

2.929  0.649 

3.905  0.866 

4.881    1.082 

30 

45 

0.975  0.221 

1.951  0.441 

2.926  0.662 

3.901   0.883 

4.877   1.103 

15 

13   0 

0.974  0225 

1.949  0.450 

2.923  0.675 

3.897  0.900 

4.872  1.125 

77   0 

15 

0.973  0229 

1.947  0.458 

2.920  0.688 

3.894  0.917 

4.867   1.146 

45 

30 

0.972  0.233 

1.945  0.467 

2.917  0.700 

3.889  0.934 

4.862   1.167 

30 

45 

0.971  0.238 

1.943  0.475 

2.914  0.713 

3.885  0.951 

4.857   1.188 

IS 

14   0 

0.970  0.242 

1.941   0.484 

2.911   0.726 

3.881  0.968 

4.851   1.210 

76   0 

15 

0.%9  0.246 

1.938  0.492 

2.908  0.738 

3.877  0.985 

4.846   1.231 

45 

30 

0.968  0.250 

1.936  0.501 

2.9(H  0.751 

3.873   1.002 

4.841   1.252 

30 

45 

0.%7  0.255 

1.934  0.509 

2.901   0.764 

3.868  1.018 

4.835   1.273 

15 

16   0 

0.966  0.259 

1.932  0.518 

2.898  0.776 

3.864  1.035 

4.830  1.294 

76   0 

O      f 

Dep.     Lat. 
Distance  1. 

Dep.      Lat. 

Dep.      Lat. 
Distance  3. 

Dep.     Lat. 
Distance  4. 

Dep.     Lat. 

o     ; 

Bearing. 

Distance  2. 

Distance  5. 

Bearing, 

76°-9(r 


o°- 

-16° 

71 

Bearing. 

Distance  6. 

Distance  7. 

Distance  8. 

Distance  9.  Distance  10. 

Bearing. 

o     f 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

o     / 

015 

6.000 

0.026 

7.000 

0.031 

8.000 

0.035 

9.000 

0.039 

10.000 

0.044 

89  45 

30 

6.000 

0.052 

7.000 

0.061 

8.000 

0.070 

9.000 

0.079 

10.000 

0.087 

30 

45 

5.999 

0.079 

6.999 

0.092 

7.999 

0.105 

8.999 

0.118 

9.999 

0.131 

15 

1    0 

5.999 

0.105 

6.999 

0.122 

7.999 

0.140 

8.999 

0.157 

9.999 

0.175 

89   0 

15 

5.999 

0.131 

6.998 

0.153 

7.998 

0.175 

8.998 

0.196 

9.998 

0.218 

45 

30 

5.998 

0.157 

6.998 

0.183 

7.997 

0.209 

8.997 

0.236 

9.997 

0.262 

30 

45 

5.997 

0.183 

6.997 

0.214 

7.996 

0.244 

8.9% 

0.275 

9.995 

0.305 

15 

2   0 

5.996 

0.209 

6.996 

0.244 

7.995 

0.279 

8.995 

0.314 

9.994 

0.349 

88   0 

15 

5.995 

0.236 

6.995 

0.275 

7.994 

0.314 

8.993 

0.353 

9.992 

0.393 

45 

30 

5.994 

0.262 

6.993 

0.305 

7.992 

0.349 

8.991 

0.393 

9.991 

0.436 

30 

45 

5.993 

0.288 

6.992 

0.336 

7.991 

0.384 

8.990 

0.432 

9.989 

0.480 

15 

3   0 

5.992 

0.314 

6.990 

0.366 

7.989 

0.419 

8.988 

0.471 

9.986 

0.523 

87   0 

15 

5.990 

0.340 

6.989 

0.397 

7.987 

0.454 

8.986 

0.510 

9.984 

0.567 

45 

30 

5.989 

0.366 

6.987 

0.427 

7.985 

0.488 

8.983 

0.549 

9.981 

0.611 

30 

45 

5.987 

0.392 

6.985 

0.458 

7.983 

0.523 

8.981 

0.589 

9.979 

0.654 

15 

4   0 

5.985 

0.419 

6.983 

0.488 

7.981 

0.558 

8.978 

0.628 

9.976 

0.698 

86  0 

15 

5.984 

0.445 

6.981 

0.519 

7.978 

0.593 

8.975 

0.667 

9.973 

0.741 

45 

30 

5.982 

0.471 

6.978 

0.549 

7.975 

0.628 

8.972 

0.706 

9.%9 

0.785 

30 

45 

5.979 

0.497 

6.976 

0.580 

7.973 

0.662 

8.%9 

0.745 

9.966 

0.828 

15 

6   0 

5.977 

0.523 

6.973 

0.610 

7.970 

0.697 

8.966 

0.784 

9.%2 

0.872 

86   0 

15 

5.975 

0.549 

6.971 

0.641 

7.966 

0.732 

8.%2 

0.824 

9.958 

0.915 

45 

30 

5.972 

0.575 

6.968 

0.671 

7.%3 

0.767 

8.959 

0.863 

9.954 

0.959 

30 

45 

5.970 

0.601 

6.%5 

0.701 

7.960 

0.802 

8.955 

0.902 

9.950 

1.002 

15 

6   0 

5.%7 

0.627 

6.%2 

0.732 

7.956 

0.836 

8.951 

0.941 

9.945 

1.045 

84   0 

IS 

5.964 

0.653 

6.958 

0.762 

7.952 

0.871 

8.947 

0.980 

9.941 

1.089 

•  45 

30 

5.%1 

0.679 

6.955 

0.792 

7.949 

0.906 

8.942 

1.019 

9.936 

1.132 

30 

45 

5.958 

0.705 

6.951 

0.823 

7.945 

0.940 

8.938 

1.058 

9.931 

1.175 

IS 

7   0 

5.955 

0.731 

6.948 

0.853 

7.940 

0.975 

8.933 

1.097 

9.926 

1.219 

83   0 

15 

5.952 

0.757 

6.944 

0.883 

7.936 

1.010 

8.928 

1.136 

9.920 

1.262 

45 

30 

5.949 

0.783 

6.940 

0.914 

7.932 

1.044 

8.923 

1.175 

9.914 

1.305 

30 

45 

5.945 

0.809 

6.936 

0.944 

7.927 

1.079 

8.918 

1.214 

9.909 

1.349 

15 

8   0 

5.942 

0.835 

6.932 

0.974 

7.922 

1.113 

8.912 

1.253 

9.903 

1.392 

82  0 

15 

5.938 

0.861 

6.928 

1.004 

7.917 

1.148 

8.907 

1.291 

9.897 

1.435 

45 

30 

5.934 

0.887 

6.923 

1.035 

7.912 

1.182 

8.901 

1.330 

9.890 

1.478 

30 

45 

5.930 

0.913 

6.919 

1.065 

7.907 

1.217 

8.895 

1.369 

9.884 

1.521 

15 

9   0 

5.926 

0.939 

6.914 

1.095 

7.902 

1.251 

8.889 

1.408 

9.877 

1.564 

81    0 

15 

5.922 

0.964 

6.909 

1.125 

7.896 

1.286 

8.883 

1.447 

9.870 

1.607 

45 

30 

5.918 

0.990 

6.904 

1.155 

7.890 

1.320 

8.877 

1.485 

9.863 

1.651 

30 

45 

5.913 

1.016 

6.899 

1.185 

7.884 

1.355 

8.870 

1.524 

9.856 

1.694 

15 

lO   0 

S.909 

1.042 

6.894 

1.216 

7.878 

1.389 

8.863 

1.563 

9.848 

1.737 

80   0 

15 

5.904 

1.068 

6.888 

1.246 

7.872 

1.424 

8.856 

1.601 

9.840 

1.779 

45 

30 

5.900 

1.093 

6.883 

1.276 

7.866 

1.458 

8.849 

1.640 

9.833 

1.822 

30 

45 

5.895 

1.119 

6.877 

1.306 

7.860 

1.492 

8.842 

1.679 

9.825 

1.865 

15 

11    0 

5.890 

1.145 

6.871 

1.336 

7.853 

1.526 

8.835 

1.717 

9.816 

1.908 

79  0 

15 

5.885 

1.171 

6.866 

1.366 

7.846 

1.561 

8.827 

1.756 

9.808 

1.951 

45 

30 

5.880 

1.196 

6.859 

1.396 

7.839 

1.595 

8.819 

1.794 

9.799 

1.994 

30 

45 

5.874 

1.222 

6.853 

1.425 

7.832 

1.629 

8.811 

1.833 

9.791 

2.036 

15 

12   0 

5.869 

1.247 

6.847 

1.455 

7.825 

1.663 

8.803 

1.871 

9.782 

2.079 

78   0 

15 

5.863 

1.273 

6.841 

1.485 

7.818 

1.697 

8.795 

1.910 

9.772 

2.122 

45 

30 

5.858 

1.299 

6.834 

1.515 

7.810 

1.732 

8.787 

1.948 

9.763 

2.164 

30 

45 

5.852 

1.324 

6.827 

1.545 

7.803 

1.766 

8.778 

1.986 

9.753 

2.207 

15 

13   0 

5.846 

1.350 

6.821 

1.575 

7.795 

1.800 

8.769 

2.025 

9.744 

2.250 

77   0 

15 

5.840 

1.375 

6.814 

1.604 

7.787 

1.834 

8.760 

2.063 

9.734 

2.292 

45 

30 

5.834 

1.401 

6.807 

1.634 

7.779 

1.868 

8.751 

2.101 

9.724 

2.335 

30 

45 

5.828 

1.426 

6.799 

1.664 

7.771 

1.902 

8.742 

2.139 

9.713 

2.377 

IS 

14   0 

5.822 

1.452 

6.792 

1.693 

7.762 

1.935 

8.733 

2.177 

9.703 

2.419 

76  0 

15 

5.815 

1.477 

6.785 

1.723 

7.754 

l.%9 

8.723 

2.215 

9.692 

2.462 

45 

30 

5.809 

1.502 

6.777 

1.753 

7.745 

2.003 

8.713 

2.253 

9.682 

2.504 

30 

45 

5.802 

1.528 

6.769 

1.782 

7.736 

2.037 

8.703 

2.291 

9.671 

2.546 

15 

16    0 

5.7% 

1.553 

6.761 

1.812 

7.727 

2.071 

8.693 

2.329 

9.659 

2.588 

76   0 

o    r 

Dep.     Lat. 
Distance  6. 

Dep.      Lat. 
Distance  7. 

Dep.      Lat. 
Distance  8. 

Dep. 

Lat. 

Dep. 

Lat. 

O       f 

Bearing. 

Distance  9. 

Distance  10. 

Bearing. 

76° -9a 


72 


16° -30' 


I 


\n 


H 


Bearing. 

Distance  1. 

Distance  2. 

Distance  3. 

Distance  4. 

Distance  5. 

Bearing. 

O       f 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat.      Dep. 

Lat. 

Dep. 

O       f 

1615 

0.965 

0.263 

1.930 

0.526 

2.894 

0.789 

3.859  1.052 

4.824 

1.315 

74  45 

30 

0.96+ 

0.267 

1.927 

0.534 

2.891 

0.802 

3.855   1.069 

4.818 

1.336 

30 

45 

0.%2 

0.271 

1.925 

0.543 

2.887 

0.814 

3.850  1.086 

4.812 

1.357 

15 

16   0 

0.%1 

0.276 

1.923 

0.551 

2.884 

0.827 

3.845   1.103 

4.806 

1.378 

74  0 

15 

0.960 

0.280 

1.920 

0.560 

2.880 

0.839 

3.840  1.119 

4.800 

1.399 

45 

30 

0.959 

0.284 

1.918 

0.568 

2.876 

0.852 

3.835   1.136 

4.794 

1.420 

30 

45 

0.958 

0.288 

1.915 

0.576 

2.873 

0.865 

3.830  1.153 

4.788 

1.441 

15 

17    0 

0.956 

0.292 

1.913 

0.585 

2.869 

0.877 

3.825    1.169 

4.782 

1.462 

73   0 

15 

0.955 

0.297 

1.910 

0.593 

2.865 

0.890 

3.820  1.186 

4.775 

1.483 

45 

30 

0.954 

0.301 

1.907 

0.601 

2.861 

0.902 

3.815   1.203 

4.769 

1.504 

30 

45 

0.952 

0.305 

1.905 

0.610 

2.857 

0.915 

3.810  1.220 

4.762 

1.524 

15 

18   0 

0.951 

0.309 

1.902 

0.618 

2.853 

0.927 

3.804   1.236 

4.755 

1.545 

72   0 

15 

0.950 

0.313 

1.899 

0.626 

2.849 

0.939 

3.799  1.253 

4.748 

1.566 

45 

30 

0.948 

0.317 

1.897 

0.635 

2.845 

0.952 

3.793   1.269 

4.742 

1.587 

30 

45 

0.947 

0.321 

1.894 

0.643 

2.841 

0.964 

3.788   1.286 

4.735 

1.607 

15 

19   0 

0.946 

0.326 

1.891 

0.651 

2.837 

0.977 

3.782   1.302 

4.728 

1.628 

71    0 

15 

0.944 

0.330 

1.888 

0.659 

2.832 

0.989 

3.776  1.319 

4.720 

1.648 

45 

30 

0.943 

0.334 

1.885 

0.668 

2.828 

1.001 

3.771   1.335 

4.713 

1.669 

30 

45 

0.941 

0.338 

1.882 

0.676 

2.824 

1.014 

3.765   1.352 

4.706 

1.690 

15 

20   0 

0.940 

0.342 

1.879 

0.684 

2.819 

1.026 

3.7.59  1.368 

4.698 

1.710 

70  0 

15 

0.938 

0.346 

1.876 

0692 

2.815 

1.038 

3.753   1.384 

4.691 

1.731 

45. 

30 

0.937 

0.350 

1.873 

0.700 

2.810 

1.051 

3.747   1.401 

4.683 

1.751 

30 

45 

0.935 

0.354 

1.870 

0.709 

2.805 

1.063 

3.741    1.417 

4.676 

1.771 

15 

21    0 

0.934 

0.358 

1.867 

0.717 

2.801 

1.075 

3.734   1.433 

4.668 

1.792 

69  0 

15 

0.932 

0.362 

1.864 

0.725 

2.7% 

1.087 

3.728  1.450 

4.660 

1.812 

45 

30 

0.930 

0367 

1.861 

0.733 

2.791 

1.100 

3.722   1.466 

4.652 

1.833 

30 

45 

0.929 

0.371 

1.858 

0.741 

2.786 

1.112 

3.715    1.482 

4.644 

1.853 

15 

22   0 

0.927 

0.375 

1.854 

0.749 

2.782 

1.124 

3.709   1.498 

4.636 

1.873 

68   0 

15 

0.926 

0.379 

1.851 

0.757 

2.777 

1.136 

3.702   1.515 

4.628 

1.893 

45 

30 

0.924 

0.38^ 

1.848 

0.765 

2.772 

1.148 

3.6%  1.531 

4.619 

1.913 

30 

45 

0.922 

0.387 

1.844 

0.773 

2.767 

1.160 

3.689   1.547 

4.611 

1.934 

15 

23   0 

0.921 

0.391 

1.841 

0.781 

2.762 

1.172 

3.682   1.563 

4.603 

1.954 

67   0 

15 

0.919 

0.395 

1.838 

0.789 

2.756 

1.184 

3.675   1.579 

4.594 

1.974 

45 

30 

0.917 

0.399 

1.834 

0.797 

2.751 

1.1% 

3.668  1.595 

4.585 

1.994 

30 

45 

0.915 

0.403 

1.831 

0.805 

2.746 

1.208 

3.661    1.611 

4.577 

2.014 

15 

24   0 

0.914 

0.407 

1.827 

0.813 

2.741 

1.220 

3.654   1.627 

4.568 

2.034 

66   0 

15 

0.912 

0.411 

1.824 

0.821 

2.735 

1.232 

3.647  1.643 

4.559 

2.054 

45 

30 

0.910 

0.415 

1.820 

0.829 

2.730 

1.244 

3.640  1.659 

4.550 

2.073 

30 

45 

0.908 

0.419 

1.816 

0.837 

2.724 

1.256 

3.633   1.675 

4.541 

2.093 

15 

25   0 

0.906 

0.423 

1.813 

0.845 

2.719 

1.268 

3.625   1.690 

4.532 

2.113 

65   0 

15 

0.90+ 

0.427 

1.809 

0.853 

2.713 

1.280 

3.618  1.706 

4.522 

2.133 

45 

30 

0.903 

0.431 

1.805 

0.861 

2.708 

1.292 

3.610  1.722 

4.513 

2.153 

30 

45 

0.901 

0.434 

1.801 

0.869 

2.702 

1.303 

3.603   1.738 

4.503 

2.172 

15 

26   0 

0.899 

0.438 

1.798 

0.877 

2.6% 

1.315 

3.595   1.753 

4.494 

2.192 

64   0 

15 

0.897 

0.442 

1.794 

0.885 

2.691 

1.327 

3.587   1.769 

4.484 

2.211 

45 

30 

0.895 

0.446 

1.790 

0  892 

2.685 

1.339 

3.580  1.785 

4.475 

2.231 

30 

45 

0.893 

0.450 

1.786 

0.900 

2.679 

1.350 

3.572  1.800 

4.465 

2.250 

15 

27   0 

0.891 

0.454 

1.782 

0.908 

2.673 

1.362 

3.564  1.816 

4.455 

2.270 

63   0 

15 

0.889 

0.458 

1.778 

0.916 

2.667 

1.374 

3.556  1.831 

4.445 

2.289 

45 

30 

0.8S7 

0.462 

1.774 

0.923 

2.661 

U85 

3.548   1.847 

4.435 

2.309 

30 

45 

0.885 

0.466 

1.770 

0.931 

2.655 

1.397 

3.540   1.862 

4.425 

2.328 

15 

28   0 

0.883 

0.469 

1.766 

0.939 

2.649 

1.408 

3.532   1.878 

4.415 

2.347 

62   0 

15 

0.881 

0.473 

1.762 

0.947 

2.643 

1.420 

3.524   1.893 

4.404 

2.367 

.45 

30 

0.879 

0.477 

1.758 

0.954 

2.636 

1.431 

3.515    1.909 

4.394 

2.386 

30 

45 

0.877 

0.481 

1.753 

0.%2 

2.630 

1.443 

3.507   1.924 

4.384 

2.405 

15 

29   0 

0.875 

0.485 

1.749 

0.970 

2.624 

1.454 

3.498   1.939 

4.373 

2.424 

61   0 

15 

0.872 

0.489 

1.745 

0.977 

2.617 

1.466 

3.490  1.954 

4.362 

2.443 

45 

30 

0.870 

0.492 

1.741 

0.985 

2.611 

1.477 

3.481   1.970 

4.352 

2.462 

30 

45 

0.868 

0.4% 

1.736 

0.992 

2.605 

1.489 

3.473   1.985 

4.341 

2.481 

15 

30   0 

0.866 

0.500 

1.732 

1.000 

2.598 

1.500 

3.464  2.000 

4.330 

2.500 

60  0 

O       f 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep.     Lat. 

Dep. 

Lat. 

o      / 

Bearing. 

Distance  1. 

Distance  2. 

Distance  3. 

Distance  4. 

Distance  5. 

Bearing. 

16° -30' 


73 


Bearing. 

Distance  6. 

Distance  7. 

Distance  8. 

Distance  9. 

Distance  10. 

Bearing. 

o     f 

Lat. 

Dep, 

Lat. 

Dep. 

Lat. 

Dep. 

Lat.      Dep. 

Lat.     Dep. 

O       f 

15  15 

5.789 

1.578 

6.754 

1.841 

7.718 

2.104 

8.683   2.367 

9.648  2.630 

74  45 

30 

5.782 

1.603 

6.745 

1.871 

7.709 

2.138 

8.673   2.405 

9.636  2.672 

30 

45 

5.775 

1.629 

6.737 

1.900 

7.700 

2.172 

8.662  2.443 

9.625   2.714 

15 

16   0 

5.768 

1.654 

6.729 

1.929 

7.690 

2.205 

8.651   2.481 

9.613  2.756 

74   0 

15 

5.760 

1.679 

6.720 

1.959 

7.680 

2.239 

8.640  2.518 

9.601   2.798 

45 

30 

5.753 

1.704 

6.712 

1.988 

7.671 

2.272 

8.629  2.556 

9.588  2.840 

30 

45 

5.745 

1.729 

6.703 

2.017 

7.661 

2.306 

8.618  2.594 

9.576  2.882 

15 

17   0 

5.738 

1.754 

6.694 

2.0+7 

7.650 

2.339 

8.607  2.631 

9.563   2.924 

73   0 

15 

5.730 

1.779 

6.685 

2.076 

7.6+0 

2.372 

8.595   2.669 

9.550  2.%5 

45 

30 

5.722 

1.804 

6.676 

2.105 

7.630 

2.406 

8.583  2.706 

9.537  3.007 

30 

45 

5.714 

1.829 

6.667 

2.134 

7.619 

2.439 

8.572  2.744 

9.524  3.049 

15 

18   0 

5.706 

1.854 

6.657 

2.163 

7.608 

2.472 

8.560  2.781 

9.511  3.090 

72   0 

15 

5.698 

1.879 

6.6+8 

2.192 

7.598 

2.505 

8.547  2.818 

9.497  3.132 

45 

30 

5.690 

1.90+ 

6.638 

2.221 

7.587 

2.538 

8.535  2.856 

9.483   3.173 

30 

45 

5.682 

1.929 

6.629 

2.250 

7.575 

2.572 

8.522  2.893 

9.469  3.214 

15 

19   0 

5.673 

1.953 

6.619 

2.279 

7.564 

2.605 

8.510  2.930 

9.455   3.256 

71    0 

15 

5.665 

1.978 

6.609 

2.308 

7.553 

2.638 

8.497   2.%7 

9.441  3.297 

45 

30 

5.656 

2.003 

6.598 

2.337 

7.541 

2.670 

8.484  3.004 

9.426  3.338 

30 

45 

5.647 

2.028 

6.588 

2.365 

7.529 

2.703 

8.471   3.041 

9.412  3.379 

15 

20   0 

5.638 

2.052 

6.578 

2.394 

7.518 

2.736 

8.457  3.078 

9.397  3.420 

70  0 

IS 

5.629 

2.077 

6.567 

2.423 

7.506 

2.769 

8.444  3.115 

9.382  3.461 

45 

30 

5.620 

2.101 

6.557 

2.451 

7.493 

2.S02 

8.430  3.152 

9367  3.502 

30 

45 

5.611 

2.126 

6.5+6 

2.480 

7.481 

2.834 

8.416  3.189 

9.351   3.543 

15 

21    0 

5.601 

2.150 

6.535 

2.509 

7.469 

2.867 

8.402  3.225 

9.336  3.584 

69   0 

15 

5.592 

2.175 

6.524 

2.537 

7.456 

2.900 

8.388  3.262 

9.320  3.624 

45 

30 

5.582 

2.199 

6.513 

2.566 

7.443 

2.932 

8.374  3.299 

9.304  3.665 

30 

45 

5.573 

2.223 

6.502 

2.594 

7.430 

2.964 

8.359  3.335 

9.288  3.706 

15 

22   0 

5.563 

2.2+8 

6.490 

2.622 

7.417 

2.997 

8.345  3.371 

9.272  3.746 

68   0 

15 

5.553 

2.272 

6.479 

2.651 

7.404 

3.029 

8.330  3.408 

9.255  3.787 

45 

30 

5.543 

2.296 

6.467 

2.679 

7.391 

3.061 

8.315  3.444 

9.239  3.827 

30 

45 

5.533 

2.320 

6.455 

2.707 

7.378 

3.094 

8.300  3.480 

9.222  3.867 

15 

23   0 

5.523 

2.344 

6.444 

2.735 

7.364 

3.126 

8.285   3.517 

9.205  3.907 

67   0 

15 

5.513 

2.368 

6.432 

2.763 

7.350 

3.158 

8.269  3.553 

9.188  3.947 

45 

30 

5.502 

2.392 

6.419 

2.791 

7.336 

3.190 

8.254  3.589 

9.171  3.988 

30 

45 

5.492 

2.416 

6.407 

2.819 

7.322 

3.222 

8.238  3.625 

9.153  4.028 

15 

24  0 

5.481 

2.440 

6.395 

2.847 

7.308 

3.254 

8.222  3.661 

9.136  4.067 

66   0 

IS 

5.471 

2.464 

6.382 

2.875 

7.294 

3.286 

8.206  3.6% 

9.118  4.107 

45 

30 

5.460 

2.488 

6.370 

2.903 

7.280 

3.318 

8.190  3.732 

9.100  4.147 

30 

45 

5.449 

2.512 

6.357 

2.931 

7.265 

3.349 

8.173  3.768 

9.081  4.187 

IS 

25   0 

5.438 

2.536 

6.344 

2.958 

7.250 

3.381 

8.157  3.804 

9.063  4.226 

65   0 

15 

5.427 

2.559 

6.331 

2.986 

7.236 

3.413 

8.140  3.839 

9.0+5  4.266 

45 

30 

5.416 

2.583 

6.318 

3.014 

7.221 

3.444 

8.123  3.875 

9.026  4.305 

30 

45 

5.404 

2.607 

6.305 

3.041 

7.206 

3.476 

8.106  3.910 

9.007  4.345 

15 

26   0 

5.393 

2.630 

6.292 

3.069 

7.190 

3.507 

8.089  3.945 

8.988  4.384 

64   0 

15 

5.381 

2.654 

6.278 

3.0% 

7.175 

3.538 

8.072  3.981 

8.%9  4.423 

45 

30 

5.370 

2.677 

6.265 

3.123 

7.160 

3.570 

8.054  4.016 

8.949  4.462 

30 

45 

5.358 

2.701 

6.251 

3.151 

7.144 

3.601 

8.037  4.051 

8.930  4.501 

15 

27    0 

5.346 

2.724 

6.237 

3.178 

7.128 

3.632 

8.019  4.086 

8.910  4.5+0 

63   0 

15 

5.334 

2.747 

6.223 

3.205 

7.112 

3.663 

8.001   4.121 

8.890  4.579 

45 

30 

5.322 

2.770 

6.209 

3.232 

7.096 

3.694 

7.983  4.156 

8.870  4.618 

30 

45 

5.310 

2.794 

6.195 

3.259 

7.080 

3.725 

7.%5  4.190 

8.850  4.656 

15 

28   0 

5.298 

2.817 

6.181 

3.286 

7.064 

3.756 

7.947  4.225 

8.829  4.695 

62   0 

15 

5.285 

2.8+0 

6.166 

3.313 

7.047 

3.787 

7.928  4.260 

8.809  4.733 

45 

30 

5.273 

2.863 

6.152 

3.340 

7.031 

3.817 

7.909  4.294 

8.788  4.772 

30 

45 

5.260 

2.886 

6.137 

3.367 

7.014 

3.8+8 

7.891  4.329 

8.767  4.810 

15 

29   0 

5.248 

2.909 

6.122 

3.394 

6.997 

3.878 

7.872  4.363 

8.746  4.8+8 

61    0 

15 

5.235 

2.932 

6.107 

3.420 

6.980 

3.909 

7.852  4.398 

8.725   +.886 

45 

30 

5.222 

2.955 

6.093 

3.447 

6.963 

3.939 

7.833  4.432 

8.704  4.924 

30 

45 

5.209 

2.977 

6.077 

3.474 

6.946 

3.970 

7.814  4.466 

8.682  4.%2 

15 

30   0 

5.1% 

3.000 

6.062 

3.500 

6.928 

4.000 

7.794  4.500 

8.660  5.000 

60  0 

O      f 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep.     Lat. 

Dep.     Lat. 

O      f 

Bearing. 

Distance  6. 

Distance  7* 

Distance  8. 

Distance  9. 

Distance  10. 

Bearing. 

60° -76 


o 


60° -76^ 


* 


i 


(' 


74 

30°- 

-46 

0 

Bearing. 

Distance  1. 

Distance  2. 

Distance  3. 

Distance  4. 

Distance  5. 

Bearing. 

o    '  f 

Lat. 

Dep. 

Lat. 

Dep. 

Lat 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

O       f 

3015 

0.864 

0.504 

1.728 

1.008 

2.592 

1.511 

3.455 

2.015 

4.319 

2.519 

59  45 

30 

0.862 

0.508 

1.723 

1.D15 

2.585 

1.523 

3.447 

2.030 

4.308 

2.538 

30 

45 

0.859 

0.511 

1.719 

1.023 

2.578 

1.534 

3.438 

2.045 

4.297 

2.556 

15 

31    0 

0.857 

0.515 

1.714 

1.030 

2.572 

1.545 

3.429 

2.060 

4.286 

2.575 

59   0 

15 

0.855 

0.519 

1.710 

1.038 

2.565 

1.556 

3.420 

2.075 

4.275 

2.594 

45 

30 

0.853 

0.522 

1.705 

1.045 

2.558 

1.567 

3.411 

2.090 

4.263 

2.612 

30 

45 

0.850 

0.526 

1.701 

1.052 

2.551 

1.579 

3.401 

2.105 

4.252 

2.631 

15 

32   0 

0.848 

0.530 

1.6% 

1.060 

2.544 

1.590 

3.392 

2.120 

4.240 

2.650 

58   0 

15 

0.846 

0.534 

1.691 

1.067 

2.537 

1.601 

3.383 

2.134 

4.229 

2.668 

45 

30 

0.843 

0.537 

1.687 

1.075 

2.530 

1.612 

3.374 

2.149 

4.217 

2.686 

30 

45 

0.841 

0.541 

1.682 

1.082 

2.523 

1.623 

3.364 

2.164 

4.205 

2.705 

15 

33   0 

0.839 

0.545 

1.677 

1.089 

2.516 

1.634 

3.355 

2.179 

4.193 

2.723 

57   0 

15 

0.836 

0.548 

1.673 

1.097 

2.509 

1.645 

3.345 

2.193 

4.181 

2.741 

45 

30 

0.834 

0.552 

1.668 

1.104 

2.502 

1.656 

3.336 

2.208 

4.169 

2.760 

30 

45 

0.831 

0.556 

1.663 

1.111 

2.494 

1.667 

3.326 

2.222 

4.157 

2.778 

15 

34   0 

0.829 

0.559 

1.658 

1.118 

2.487 

1.678 

3.316 

2.237 

4.145 

2.7% 

56  0 

15 

0.827 

0.563 

1.653 

1.126 

2.480 

1.688 

3.306 

2.251 

4.133 

2.814 

45 

30 

0.824 

0.566 

1.618 

1.133 

2.472 

1.699 

3.297 

2.266 

4.121 

2.832 

30 

45 

0.822 

0.570 

1.643 

1.140 

2.465 

1.710 

3.287 

2.280 

4.108 

2.850 

15 

35   0 

0.819 

0.574 

1.638 

1.147 

2.457 

1.721 

3.277 

2.294 

4.0% 

2.868 

55   0 

15 

0.817 

0.577 

1.633 

1.154 

2.450 

1.731 

3.267 

2.309 

4.083 

2.886 

45 

30 

0.814 

0.581 

1.628 

1.161 

2.442 

1.742 

3.257 

2.323 

4.071 

2.904 

30 

45 

0.812 

0.584 

1.623 

1.168 

2.435 

1.753 

3.246 

2.337 

4.058 

2.921 

15 

36   0 

0.809 

0.588 

1.618 

1.176 

2.427 

1.763 

3.236 

2.351 

4.045 

2.939 

54   0 

15 

0.806 

0.591 

1.613 

1.183 

2.419 

1.774 

3.226 

2.365 

4.032 

2.957 

45 

30 

0.804 

0.595 

1.608 

1.190 

2.412 

1.784 

3.215 

2.379 

4.019 

2.974 

30 

45 

0.801 

0.598 

1.603 

1.197 

2.404 

1.795 

3.205 

2.393 

4.006 

2.992 

15 

37   0 

0.799 

0.602 

1.597 

1.204 

2.3% 

1.805 

3.195 

2.407 

3.993 

3.009 

53  0 

15 

07% 

0.605 

1.592 

1.211 

2.388 

1.816 

3.184 

2.421 

3.980 

3.026 

45 

30 

0.793 

0.609 

1.587 

1.218 

2.380 

1.826 

3.173 

2.435 

3.%7 

3.044 

30 

45 

0.791 

0.612 

1.581 

1.224 

2.372 

1.837 

3.163 

2.449 

3.953 

3.061 

15 

38   0 

0.788 

0.616 

1.576 

1.231 

2.364 

1.847 

3.152 

2.463 

3.940 

3.078 

52   0 

15 

0.785 

0.619 

1.571 

1.238 

2.356 

1.857 

3.141 

2.476 

3.927 

3.095 

45 

30 

0.783 

0.623 

1.565 

1.245 

2.348 

1.868 

3.130 

2.490 

3.913 

3.113 

30 

45 

0.780 

0.626 

1.560 

1.252 

2.340 

1.878 

3.120 

2.504 

3.899 

3.130 

15 

39   0 

0.777 

0.629 

1.554 

1.259 

2331 

1.888 

3.109 

2.517 

3.886 

3.147 

51    0 

15 

0.774 

0.633 

1.549 

1.265 

2.323 

1.898 

3.098 

2.531 

3.872 

3.164 

45 

30 

0.772 

0.636 

1.543 

1.272 

2.315 

1.908 

3.086 

2.544 

3.858 

3.180 

30 

45 

0.769 

0.639 

1.538 

1.279 

2.307 

1.918 

3.075 

2.558 

3.844 

3.197 

15 

40   0 

0.766 

0.643 

1.532 

1.286 

2.298 

1.928 

3.064 

2.571 

3.830 

3.214 

50   0 

15 

0.763 

0.6+6 

1.526 

1.292 

2.290 

1.938 

3.053 

2.584 

3.816 

3.231 

45 

30 

0.760 

0.649 

1.521 

1.299 

2.281 

1.948 

3.042 

2.598 

3.802 

3.247 

30 

45 

0.758 

0.653 

1.515 

1.306 

2.273 

1.958 

3.030 

2.611 

3.788 

3.264 

15 

41    0 

0.755 

0.656 

1.509 

1.312 

2.264 

1.968 

3.019 

2.624 

3.774 

3.280 

49   0 

15 

0.752 

0.659 

1.504 

1.319 

2.256 

1.978 

3.007 

2.637 

3.759 

3.297 

45 

30 

0.749 

0.663 

1.498 

1325 

2.247 

1.988 

2.9% 

2.650 

3.745 

3.313 

30 

45 

0.746 

0.666 

1.492 

1.332 

2.238 

1.998 

2.984 

2.664 

3.730 

3.329 

15 

42   0 

0.743 

0.669 

1.486 

1.338 

2.229 

2.007 

2.973 

2.677 

3.716 

3.346 

48    0 

15 

0.740 

0.672 

1.480 

1.345 

2.221 

2.017 

2.%1 

2.689 

3.701 

3.362 

45 

30 

0.737 

0.676 

1.475 

1.351 

2.212 

2.027 

2.949 

2.702 

3.686 

3.378 

30 

45 

0.734 

0.679 

1.469 

1.358 

2.203 

2.036 

2.937 

2.715 

3.672 

3394 

15 

43   0 

0.731 

0.682 

1.463 

1.364 

2.194 

2.046 

2.925 

2.728 

3,657 

3.410 

47   0 

15 

0.728 

0.685 

1.457 

1.370 

2.185 

2.056 

2.913 

2.741 

3.642 

3.426 

45 

30 

0.725 

0.688 

1.451 

1.377 

2.176 

2.065 

2.901 

2.753 

3.627 

3.442 

30 

45 

0.722 

0.692 

1.445 

1.383 

2.167 

2.075 

2.889 

2.766 

3.612 

3.458 

15 

44    0 

0.719 

0.695 

1.439 

1.389 

2.158 

2.084 

2.877 

2.779 

3.597 

3.473 

46   0 

15 

0.716 

0.698 

1.433 

1.3% 

2.149 

2.093 

2.865 

2.791 

3.582 

3.489 

45 

30 

0.713 

0.701 

1.427 

1.402 

2.140 

2.103 

2.853 

2.804 

3.566 

3.505 

30 

45 

0.710 

0.704 

1.420 

1.408 

2.131 

2.112 

2.841 

2.816 

3.551 

3.520 

15 

45   0 

0.707 

0.707 

1.414 

1.414 

2.121 

2.121 

2.828 

2.828 

3.536 

3.536 

45   0 

0      f 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

O       f 

Bearing. 

Distance  1. 

Distance  2. 

Distance  3. 

Distance  4. 

Distance  5. 

Bearing. 

46° -60' 


k 


30°- 

-46 

o 

75 

Bearing. 

Distance  6. 

Distance  7* 

Distance  8. 

Distance  9. 

Distance  10. 

Bearing. 

o      f 

Lat. 

Dep, 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

o     t 

3015 

5.183 

3.023 

6.047 

3.526 

6.911 

4.030 

7.775 

4.534 

8.638 

5.038 

59  45 

30 

5.170 

3.045 

6.031 

3.553 

6893 

4.060 

7.755 

4.568 

8.616 

5.075 

30 

45 

5.156 

3.068 

6.016 

3.579 

6875 

4.090 

7.735 

4.602 

8.594 

5.113 

15 

31    0 

5.143 

3.090 

6.000 

3.605 

6857 

4.120 

7.715 

4.635 

8.572 

5.150 

59  0 

15 

5.129 

3.113 

5.984 

3.631 

6839 

4.150 

7.694 

4.669 

8.549 

5.188 

45 

30 

5.116 

3.135 

5.968 

3.657 

6.821 

4.180 

7.674 

4.702 

8.526 

5.225 

30 

•       45 

5.102 

3.157 

5.952 

3.683 

6.803 

4.210 

7.653 

4.736 

8.504 

5.262 

15 

32    0 

5.088 

3.180 

5.936 

3.709 

6784 

4.239 

7.632 

4.769 

8.481 

5.299 

58   0 

15 

5.074 

3.202 

5.920 

3.735 

6766 

4.269 

7.612 

4.802 

8.457 

5336 

45 

30 

5.060 

3.224 

5.904 

3.761 

6747 

4.298 

7.591 

4.836 

8.434 

5373 

30 

45 

5.046 

3.246 

5.887 

3.787 

6.728 

4328 

7.569 

4.869 

8.410 

5.410 

15 

33   0 

5.032 

3.268 

5.871 

3.812 

6.709 

4357 

7.548 

4.902 

8.387 

5.446 

57   0 

15 

5.018 

3.290 

5.854 

3.838 

6.690 

4386 

7.527 

4.935 

8.363 

5.483 

45 

30 

5.003 

3312 

5.837 

3.864 

6.671 

4.416 

7.505 

4.%7 

8339 

5.519 

30 

45 

4.989 

3.333 

5.820 

3.889 

6.652 

4.445 

7.483 

5.000 

8315 

5.556 

15 

34   0 

4.974 

3355 

5.803 

3.914 

6632 

4.474 

7.461 

5.033 

8.290 

5.592 

56   0 

15 

4.960 

3.377 

5.786 

3.940 

6613 

4.502 

7.439 

5.065 

8.266 

5.628 

45 

30 

4.945 

3398 

5.769 

3.965 

6593 

4.531 

7.417 

5.098 

8.241 

5.664 

30 

45 

4.930 

3.420 

5.752 

3.990 

6.573 

4.560 

7.395 

5.130 

8.217 

5.700 

15 

35    0 

4.915 

3.441 

5.734 

4.015 

6553 

4.589 

7372 

5.162 

8.192 

5.736 

55   0 

15 

4.900 

3.463 

5.716 

4.040 

6533 

4.617 

7350 

5.194 

8.166 

5.772 

45 

30 

4.885 

3.484 

5.699 

4.065 

6513 

4.646 

7327 

5.226 

8,141 

5.807 

30 

45 

4.869 

3.505 

5.681 

4.090 

6.493 

4.674 

7.304 

5.258 

8.116 

5.843 

IS 

36   0 

4.854 

3.527 

5.663 

4.115 

6472 

4.702 

7.281 

5.290 

8.090 

5.878 

54   0 

15 

4.839 

3.548 

5.645 

4.139 

6.452 

4.730 

7.258 

5322 

8.064 

5.913 

45 

30 

4.823 

3.569 

5.627 

4.164 

6.431 

4.759 

7.235 

5.353 

8.039 

5.948 

30 

45 

4.808 

3.590 

5.609 

4.188 

6.410 

4.787 

7.211 

5.385 

8.013 

5.983 

15 

37   0 

4.792 

3.611 

5.590 

4.213 

6.389 

4.815 

7.188 

5.416 

7.986 

6018 

63   0 

15 

4.776 

3.632 

5.572 

4.237 

6.368 

4.842 

7.164 

5.448 

7.960 

6.053 

45 

30 

4.760 

3.653 

5.554 

4.261 

6347 

4.870 

7.140 

5.479 

7.934 

6.088 

30 

45 

4.744 

3.673 

5.535 

4.286 

6.326 

4.898 

7.116 

5.510 

7.907 

6122 

15 

38   0 

4.728 

3.694 

5.516 

4310 

6304 

4.925 

7.092 

5.541 

7.880 

6157 

52   0 

15 

4.712 

3.715 

5.497 

4334 

6.283 

4.953 

7.068 

5.572 

7.853 

6191 

45 

30 

4.696 

3.735 

5.478 

4358 

6.261 

4.980 

7.043 

5.603 

7.826 

6225 

30 

45 

4.679 

3.756 

5.459 

4381 

6.239 

5.007 

7.019 

5,633 

7.799 

6259 

15 

39   0 

4.663 

3.776 

5.440 

4.405 

6217 

5.035 

6.994 

5.664 

7.772 

6.293 

51    0 

IS 

4.646 

3.7% 

5.421 

4.429 

6195 

5.062 

6.970 

5.694 

7.744 

6327 

45 

30 

4.630 

3.816 

5.401 

4.453 

6173 

5.089 

6.945 

5.725 

7.716 

6.361 

30 

45 

4.613 

3.837 

5.382 

4.476 

6151 

5.116 

6.920 

5.755 

7.688 

6394 

15 

40   0 

4.5% 

3.857 

5362 

4.500 

6128 

5.142 

6.894 

5.785 

7.660  6.428 

50   0 

15 

4.579 

3.877 

5.343 

4.523 

6106 

5.169 

6.869 

5.815 

7.632 

6.461 

45 

30 

4.562 

3.897 

5.323 

4.546 

6.083 

5.1% 

6844 

5.845 

7.604 

6.495 

30 

45 

4.545 

3.917 

5.303 

4.569 

6.061 

5.222 

6.818 

5.875 

7.576 

6528 

15 

41    0 

4.528 

3.936 

5.283 

4.592 

6.038 

5.248 

6792 

5.905 

7.547 

6561 

49   0 

15 

4.511 

3.956 

5.263 

4.615 

6.015 

5.275 

6767 

5.934 

7.518 

6594 

45 

30 

4.494 

3.976 

5.243 

4.638 

5.992 

5.301 

6741 

5.964 

7.490 

6.626 

30 

45 

4.476 

3.995 

5.222 

4.661 

5.968 

5.327 

6715 

5.993 

7.461 

6.659 

15 

42   0 

4.459 

4.015 

5.202 

4.684 

5.945 

5353 

6.688 

6022 

7.431 

6.691 

48    0 

15 

4.441 

4.034 

5.182 

4.707 

5.922 

5379 

6.662 

6.051 

7.402 

6724 

45 

30 

4.424 

4.054 

5.161 

4.729 

5.898 

5.405 

6635 

6.080 

7373 

6756 

30 

45 

4.406 

4.073 

5.140 

4.752 

5.875 

5.430 

6.609 

6109 

7343 

6788 

15 

43   0 

4.388 

4.092 

5.119 

4.774 

5.851 

5.456 

6582 

6138 

7314 

6820 

47   0 

15 

4.370 

4.111 

5.099 

4.796 

5.827 

5.481 

6555 

6167 

7.284 

6852 

45 

30 

4352 

4.130 

5.078 

4.818 

5.803 

5.507 

6528 

6195 

7.254 

6884 

30 

45 

4.334 

4.149 

5.057 

4.841 

5.779 

5.532 

6501 

6.224 

7.224 

6.915 

IS 

44   0 

4316 

4.168 

5.035 

4.863 

5.755 

5.557 

6.474 

6252 

7.193 

6947 

46   0 

15 

4.298 

4.187 

5.014 

4.885 

5.730 

5.582 

6447 

6.280 

7.163 

6.978 

45 

30 

4.280 

4.206 

4.993 

4.906 

5.706 

5.607 

6.419 

6.308 

7.133 

7.009 

30 

45 

4.261 

4.224 

4.971 

4.928 

5.681 

5.632 

6392 

6336 

7.102 

7.040 

15 

45    0 

4.243 

4.243 

4.950 

4.950 

5.657 

5.657 

6.364 

6.364 

7.071 

7.071 

45   0 

o     f 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

o     t 

Bearing. 

Distance  6. 

Distance  7. 

Distance  8. 

Distance  9. 

Distance  10. 

Bearing.  1 

46° -60' 


Hi 


\ 


A  TABLE  OF  THE  ANGLES 

Which  every  Point  and  Quarter  Point  of  the  Compass  makes  with  the  Meridian. 


NortlL. 

Points. 

.-4 

0    t    II 

2  48  45 

5  37  30 

8  26  15 

11  15    0 

Points. 

S:| 

South..                 1 

N.  by  E. 

N.by  W. 

S.  by  E. 

S.  by  W. 

N.N.E. 

N.N.^W. 

1-% 

1-J4 

2      * 

14    3  45 
16  52  30 
19  41  15 
22  30    0 

P 

S.S.E. 

S-S-W. 

N:E.byN. 

N.W.byN. 

1:1 

25  18  45 
28    7  80 
30  56  15 
33  45    0 

2 -1/4 

2-% 
3 

S.E.  by  S. 

S.W.  by  S. 

N.E. 

N.W. 

3-% 
3-% 
3-% 
4 

36  33  45 
39  22  30 
42  11  15 
45    0    0 

El 

S.E. 

S-TTV. 

N.E.byE. 

N.'W.by'W. 

4-3^ 

47  48  45 
50  37  30 
53  26  15 
56  15    0 

1^1 

S.E.  by  E. 

S.W.byW. 

E.N.E. 

■W-N.-W. 

59    3  45 
61  62  30 
64  41  15 
67  30    0 

5-% 

6-U 

6      * 

E.S.E. 

w.s.-w. 

E.  by  N. 

W.  by  N. 

6-14 
6-% 
7 

70  18  45 
73    7  30 
75  56  15 
78  46    0 

i:| 

E.  by  S. 

W.  by  S. 

East. 

West. 

7-% 

81  33  45 
84  22  30 
87  11  15 
90    0    0 

11 

East. 

"West. 

(: 


III 


'    ?R 


\ 


/vkH   o/Ic-S'I. 


MAY  031994 


COLUMBIA  UNIVERSIT|r  LIB]J{^^^^^ 


0041417275 


^^^■^■■:. 


"%*    *1"   ! 


3.-*:1 


.** 


l-W^'' 


..'•'■  f^- 


■'  ■'M 


.PR 


'^11,^ 


i>ra 


-v^ 


.iSi 


W^ 


.-.?■' 


1^ 


I 

I 

4 

I 

=1 


•'?i? 


■^^^■^' 


END  OF 
TITLE 


